To give a rather quick and dirty answer, yes there was a Polish Communist Party in interwar Poland, but it was illegal for the entire period in question. Given that the Soviet Union attempted to invade Poland (and set up a puppet communist government in expectation of success in 1920) and were only driven back once they had reached Warsaw, it's perhaps unsurprising that the Communist Party was suppressed in these years, even before Poland became a dictatorship in 1926. It remained active as an urban, largely underground organisation that struggled to achieve broad popularity. It didn't help that they were generally viewed as alien, both in terms of their obvious connections to Soviet Russia, where many of the Polish communist leaders were based, but also because the Party had disproportionately large numbers of Jewish members (perhaps 30% of the Party were Jews). The membership was never large (one source I've seen gives their numbers as peaking at 12,000 in 1931, with an additional 9,100 in their youth movement), and relatively few came from the classes they 'should' have, such as the urban proletariat or casual rural labourers.

To overcome their illegality, the Polish Communist Party attempted to use front organisations and penetrate other (legal) left-wing political parties. Their success here was mixed, winning just a couple of seats in the 1921 elections, but by establishing new front parties and soliciting defections from other parties, grew this to 23 members in 1923. After the Pidulski coup in 1926, the parliament mattered less and less in any case. Following the shift to the Popular Front strategy mandated by the Comintern in 1934, the Polish communists tried to reach out to other left-wing groups to establish a united front, but were rebuffed.

The Polish Communist Party itself became a victim of Stalin's purges during the later 1930s. I'm not well-versed enough in their history to chart the various twists and turns, but I gather that the Polish Communist Party was heavily embroiled in the factional disputes within the Soviet Union during the 1920s, which took its toll on the Party's political unity, but also made them objects of suspicion in the new Stalinist political climate of the 1930s. What's more, as so many senior Polish communists were based in or near the Soviet Union, they were much more easy for Stalin to reach than other foreign communists, and almost all of those who fell under suspicion were eventually arrested under various pretexts (most commonly as spies for the Polish government), and liquidated. I don't think any of their major leaders survived. Even after these purges, Stalin decided that none of the Polish communists could be trusted, and dissolved the entire party in March 1938.

So, to relate it back to the your previous post - the idea that Polish Communists were killing Germans in the Danzig Corridor in 1939 is absolutely ridiculous. They were never strong enough in interwar Poland to be leading or even significantly participating in the repression of the German minority, and in any case had already been effectively repressed themselves by the Polish and Soviet governments by 1939.

Sources

Much of my knowledge of Polish communism was gained incidentally through the work of Gerben Zaagsma, but I referred to a rather old piece by Richard Starr, who gave quite a narrative summary in 'The Polish Communist Party 1918-1948', Polish Review 1:2-3 (1956), pp. 41-58. This is likely to be out of date in terms of its specific interpretations, but should be fairly reliable for the kind of overview I was trying to give.