To expand a bit on an answer I wrote elsewhere today:
Essentially the reason that the USSR was able to retain the eastern parts of Interwar Poland after 1945 was because the Allies at the Potsdam Conference agreed to recognize the Communist-dominated Provisional Government of National Unity as Poland's legitimate government (the recognition came in return for promises of "free and fair elections", which never happened). That government then signed a border treaty with the USSR in August 1945 that recognized the Soviet annexation, with a few minor border adjustments.
Population movement and mass deaths during the war, plus massive population transfers after, meant that overall there weren't a lot of people left on each respective side of the border who were very interested in changing it.
The big difference between this (and the annexation of Bessarabia from Romania), from, say, the annexation of the Baltic states (which Western countries did not recognize), is that internationally-recognized governments agreed to the border changes by treaty with the USSR (Romania recognized the border changes in the 1947 Paris Peace Treaties), despite the lack of options these governments might have had in reality.
The postwar borders were granted a sort of official Europe-wide recognition in the 1975 Helsinki Accords, which included a section on "territorial integrity" of signing states. A major point of detente in the 1970s revolved around recognizing to some degree the borders in Eastern Europe as they had been drawn post-1945 (Willy Brandt's "Ostpolitik" in this period had also emphasized this).
Interestingly, with the fall of communism, not only did Poland not re-enter into border disputes with its Eastern neighbors, but under Foreign Minister Krzysztof Skubiszewski (1989-1993) it worked to develop warm relations with Ukraine and Belarus before they even became independent under what was known as a "two-track policy".
Poland signed a state-to-state "declaration" with the Ukrainian SSR in October 1990 on Skubiszewski's visit to Kiev, confirming support for the current borders (among other things, such as mutual protection for national minorities), and a similar declaration was signed the same month on Skubiszewski's visit to the Belorussian SSR. Somewhat confusingly, the Belorussians did not want their statement to confirm inviolability of the borders - they argued that the Belorussian SSR wasn't a signatory to the USSR-Poland treaty and therefore could not do so (with the Soviet Socialist Republics declaring sovereignty in 1990 and establishing their own foreign policies, it became a little confusing to determine just who was in charge). The Polish minority in the Belorussian SSR was also larger in absolute terms and in relative terms than the Polish minority in Ukraine, and this was an area of top concern for the Polish government - treatment of the minority and establishment of better trade relations were in any case a higher priority than adjusting the borders. The Polish government was also generally supportive of non-communist independence movements at the time, such as Rukh in Ukraine. Indeed, the most difficult dispute with a former Soviet Socialist Republic was actually with Lithuania, which wanted a formal apology from Poland for "occupying" Vilnius in 1920.
One major reason that Krzysztof Skubiszewski pursued this "two-track" policy with the SSRs even before the USSR dissolved, concerned with mutual respect for national minority rights, but also for not adjusting the postwar borders, was because it was facing the exact same issues with a reunited Germany in its West. Any calls for territorial adjustments in the East would call into question the 1990 Agreement by which Germany gave up East Prussia, Pomerania, and Silesia, in return for special rights granted to the remaining German minority in the Opole region. Polish policy therefore sought to respect the borders in the East in the same manner that German reunification agreed to respect the borders in the West.
Sources:
Timothy Snyder. Reconstruction of Nations
Not only Belarus, but Ukraine as well. The Soviet-Polish war of 1919-1921 resulted in Poland becoming in the end bigger than it had started and absorbing ethnic minorities in its new territory (Belarusians and Ukrainians). The border Poland got from end of WW1 was called the Curzon line, named after the British foreign secretary. The border it got from the end of the Soviet Polish war was further eastward than the Curzon line. During WW2 (Soviet invasion of Poland of 1939) and after it the Soviets reclaimed the territory that had been taken from then during the Soviet-Polish War. After the war ended, forced populaton movements were done to make the territories more ethnically homogeneous, with Poles being kicked from the eastern parts of their former country, the same happening with Germans as compensation (Germany got smaller after the war and historical German territories were ceded to Poland, with all the Germans in it kicked out).
I'm going to focus more on the second half of the question (did Poles and Belarusians have territorial disputes in the interwar period), as I feel it helps answer the first part as well (why did the USSR annex parts of Poland after 1945).
Poland was re-established as an independent state in 1918, in the aftermath of the First World War (notably it declared independence on November 11, 1918, which is obviously the day the armistice came into effect). However in the chaos of the immediate postwar era borders were not easily defined, especially in the east, which was reeling from the Russian Revolution and Treaty of Brest-Litovsk, which had nominally granted independence to several former peoples within the Russian Empire, not to mention the Russian Civil War itself. So Poland was immediately fighting for both its very survival, and to expand its territory to encompass as much as possible, with the hope that by holding said territory they would be able to press their claim at the coming peace conference to be held in Paris.
Up to 1921 Poland fought wars with Ukrainian, Lithuanian, and Russian forces, and managed to do quite well. The 1920 Battle of Warsaw, known as the “Miracle on the Vistula,” saw Polish forces defeat a Soviet invasion, and largely settled the Polish-Soviet War, in that the Soviet forces were not going to occupy Poland. This war is the key to answering the question here, as it was during this war that Poland occupied several major cities in the region, including Lwów (now Lviv in Ukraine), Wilno (Vilnius in Lithuania), Minsk, and Kyiv. While the first two cities had a significant Polish (and Jewish; noted because they were roughly 30% Jewish each) population, and not many Lithuanians or Ukrainians, Minsk and Kyiv had few Poles and more of their titular nationalities (Belarusian and Ukrainian, respectively; plus a substantial Jewish community in each). Large parts of what is now Western Belarus was also occupied by Poland.
The Treaty of Riga that ended the Polish-Soviet War gave Lwów and Wilno (I’m using the Polish versions here as that is how they were known at the time) to Poland, as well as Western Belarus, while Minsk was handed back to the Soviets (Kyiv had only been occupied briefly). The surrender of the two cities upset the Ukrainian and Lithuanian populations, who regarded them as important to their culture; independent Lithuania even declared Vilnius (as they called Wilno, and still do) their capital, though they used Kaunas as a temporary. However as noted they were mainly Polish and Jewish cities, which is what the Poles argued to justify their occupation of them. The same was said of the parts of Belarus occupied, with it further justified on account of the supposed lack of national consciousness of the Belarusian people, so not deserving of their own state. To counter this the Soviets created the Belarusian SSR, which was one of the founding republics of the USSR, thus giving the Belarusians a quasi-national state to look towards.
Anyways, it should be noted that during the Polish-Soviet War the Western Powers were deeply concerned with the outcome, as they did not want the Bolsheviks to move West, but also distrusted a strong Poland. A proposal of a border between the two was proposed by Lord Curzon, the British Foreign Secretary. Poland nearly agreed to it during the war, as they sought help from the West to defeat the Soviets; however as they started to win and move their territory East, they disregarded it, and the Treaty of Riga saw their border some 250km East of the so-called Curzon Line.
With the border effectively settled in 1921, it saw the Belarusians split between Poland and the USSR (the Ukrainians were also split, while the Lithuanians wanted Vilnius back). This did cause trouble, and throughout the 1930s the Soviets were concerned about their ethnic Polish citizens near the border, as they felt the Poles would serve as spies and lead insurrections. In that light the Soviets did support ethnic Belarusians and Ukrainians in Poland in trying to agitate the Polish state, in effect doing the thing they were concerned about. Considering that according to the 1931 Polish census 14% of the population was Ukrainian and 3% Belarusian, there were significant minorities to work with.
This agitation lasted until the outbreak of the Second World War. When the Soviets invaded Poland in 1939, they immediately annexed parts of Poland: the Western Belarusian areas and the land around Lwów, with the argument being they were uniting the Belarusian and Ukrainian peoples. Though this was undone with the German invasion in 1941 and subsequent fighting, when the Soviet forces re-occupied the area in 1944 the borders were again shifted West, and Wilno was incorporated into Lithuania (which itself had been occupied and annexed by the USSR in 1940), finally becoming Vilnius and the Lithuanian capital.
As to why the Soviets were able to do so, they pretty much cited the Curzon Line as their justification, as it very closely matched the post-1945 borders. It was hard for the British and Americans to argue against that considering it was the British who created the initial proposal and steadfastly held to it during the 1920s. I’d also argue it was necessary to agree to that in order to keep the Soviets allied with the West, as Stalin probably could have extracted more if he really tried to.
For some sources or further reading, I'd suggest the following:
Norman Davies, God's Playground: A History of Poland, Volume II: 1795 to the Present. This is the second of his two-volume history of Poland, which is pretty much the standard text on Polish history in English. There's a good amount on the interwar period and the Second Polish Republic in there.
Jerzy Borzęcki, The Soviet-Polish Peace of 1921 and the Creation of Interwar Europe. Borzęcki's book, which derives from his PhD dissertation, explicitly looks at the Treaty of Riga and its aftermath, including the negotiations leading to it and the way it divided the people there.
Timothy Snyder, The Reconstruction of Nations: Poland, Ukraine, Lithuania, Belarus, 1569–1999. Snyder is well-known for his work on the region, and this book does look at the way the various nationalities interacted with each other, especially during times of conflict.
Terry Martin, The Affirmative Action Empire: Nations and Nationalism in the Soviet Union, 1923-1939. While mainly about Soviet nationality policy, it does look at the impact of the Polish-Soviet border and how it was utilised in the Soviet Union to play up the ethnic dimensions there.
Christoph Mick, Lemberg, Lwów, L'viv, 1914–1947: Violence and Ethnicity in a Contested City. Obviously more focused on what is now called Lviv, this does look at the implications of the divisions caused by the Treaty of Riga and the interwar conflict. Originally published in German so it's an even more rigid read than other academic works.
Ideally I'd like to include a book on the history of Belarus as well, but I honestly can't think of any in particular. I'm inclined to suggest The Rise and Fall of Belarusian Nationalism, 1906–1931 by Per Anders Rudling but I haven't read it so can not do so in good faith. However I will note it comes from the University of Pittsburgh Press, who are known as a leading publisher on Eastern European history, so it may be valuable to read into.