They were some of the main reasons, but it is impossible to say if they were the exclusive reasons.

I'll answer your three questions specifically.

Knew that USA was not able to have a lot of nuclear bombs.

Even if we were to ignore the famous captured American pilot account, this falls apart on two counts:

1. The US was regularly producing nuclear weapons. This transcript between Hull and Seaman discusses a third nuclear weapon was ready to ship out on 13 August and to be dropped on 19 August. Three or four would be ready in September, another three in October. Total of nine or ten available to drop on Japan by 1 November.

2. While Japan didn't know the exact US nuclear weapons production capabilities, they did know American production far exceeded their own in other areas. Thus prudence would demand you assume the enemy can produce more weapons, and two bombs in three days is good evidence to suggest the US can build many.

There is, however, a kernel of truth here: some Japanese leaders thought there were few bombs available. It appears Army Minister Anami thought the Hiroshima bomb was the "a was the only atomic bomb the United States possessed" at 1PM on 9 August, when news of Nagasaki entered the cabinet meeting. The sources are clear, however, that this was not a common view and make it clear that others in the leadership were convinced even before Nagasaki that more were on the way, including Togo and Hirohito. As the summary below states, "the political impact of the Nagasaki bomb cannot be denied. Army Minister Anami's wishful thinking was shattered; if two bombs were available, then maybe there were three or even four."

Wanted to surrender on good terms(having all the territory they conquered before and throughout WWII).

I have never seen any source make this claim.

By August 1945 Japan had lost most of their captured territory. The Philippines were almost entirely retaken, as were many Central and Southern Pacific islands (those that had not been bypassed). The captured Dutch and British colonies would not be expected to stay Japanese under any conceivable reality.

Most historians, as summarized here, agree the Japanese War Council was, at the time of the Nagasaki Attack, split between two camps. One, led by Prime Minister Togo, "forcefully stated that Japan must immediately accept the Potsdam terms with the sole condition being that the Allies 'guarantee the emperor's position.'" The second group, led by Anami, insisted on more:

Anami insisted not only on the preservation of the imperial institution but also on the "three additional condi- tions": (1) that there be no military occupation of the homeland by the Allies; (2) that the armed forces be allowed to disarm and demobilize themselves voluntarily; and (3) that war criminals be prosecuted by the Japanese government. These were "absolute" conditions, Anami said, and Chief of the Army General Staff Umezu Yoshijiro and Chief of the Naval General Staff Toyoda supported Anami.

If you can provide a source on keeping their possessions, I'll gladly read it. However, based on the available evidence it appears that was at best wishful thinking by a handful of leaders, but sources I have don't mention it.

Hiroshima and Nagasaki weren't even the most damaged cities.

This was true, but it misses a critical point.

Usually the firebombing raid on Tokyo is most often cited, the deadliest raid of the war. Some 279 B-29s attacked the city on 10 March with 1500 metric tons of incendiaries. Other cities were struck be similar raids and were in ruins.

Hiroshima and Nagasaki were attacked by one aircraft dropping one bomb.

A large raid could be detected and countermeasures prepared. The Japanese had early warning radar sets by this time (Postwar US report on land-based sets, including schematics) that could detect these large raids and vector in fighters. But a single aircraft was more difficult to detect and could not be detected until it was much closer, providing less warning and thus ability to respond. Moreover, the raid would be over more quickly: the Tokyo raid lasted 90 minutes, Hiroshima six.

On the scale of most devastating, other cities bear mention, and in a debate on the morality of the attacks including these cities is important. But in a discussion of the military effectiveness and the Japanese ability to respond, an atomic bomb is far more difficult to stop.

This brings us to what isn't a question, but should be:

The main point of the video is the reason why Japan surrendered was that Soviets destroyed Japanese Army under Manchuria.

It's impossible to know that with certainty.

What we do know is the Japanese War Council called a meeting to discuss surrender after the Hiroshima attack, with Hirohito stating "my wish is to make such arrangements as will end the war as soon as possible." Before the meeting began news reached the members that the Soviet Union had entered the war (dawn meeting started at 10:30). During the meeting (1:00) news of the Nagasaki attack came in.

The War Council was stuck in a three-to-three deadlock when they adjourned. Two emergency cabinet meetings at 2:30 and 6PM were also deadlocked. After the Soviets crushed the Manchurian armies and two Atomic Bombs it took Hirohito to break this stalemate at 2:30 AM on 10 August. Even together these "twin shocks" as they are so often called were not enough to force Japanese surrender.

To know which played a more important role, we'd have to read Hirohito's mind on 9 and 10 August as he debated and ultimately made this decision. We can't. He did specifically cite the atomic bombs, but that does not mean the Soviets were not a major part of his decision. It is nearly impossible to find any historical event that happened mainly for one reason, and this is no exception. Any argument that tries to claim one was definitely "the main reason", whether the nukes or Soviets, is difficult to back up at best, and at worst making the situation political (usually in service of a debate on the morality of the bombings).

Bias:

While I cannot prove it, I personally believe the nukes were more important to Hirohito, somewhere between 60-40 and 75-25. The available (if circumstantial) evidence, especially his statements before the Soviet intervention, suggests this motivated him to end the war more quickly. It certainly motivated others, like Suzuki, but not all, like Anami. However, it is impossible to know whether I am right or wrong, though this does potentially color my interpretation of the evidence.

I also believe the atomic bombs were the least horrific of a series of horrific options the Allies had to force the Japanese surrender. The invasion forces were actively being prepared and would be bolstered by nukes on the beachhead, and even conservative estimates put the number of American and Japanese dead over the two nuclear bombs. Continued firebombing raids would likewise have killed more. The Japanese rice crop had failed and they were faced with a major famine, complicating both attack options. The idea of a demonstration runs into several logistic difficulties, such as selecting a target that kills the minimum number of people, showed the maximum devastation, let's the most people see the destruction and spread the news, and keeps it secret so the Japanese didn't attempt to stop the attack or truck in civilians and POWs to make the demonstration deadly and political. We also know that the nuclear bombs AND Soviets were not enough to force a surrender, so claiming the Soviets alone could do the job falls apart on examining the evidence (which I presume was a conclusion of the video you saw).

I have tried to be as neutral as possible, sticking purely to facts, but one can never completely remove bias from the equation. On something this controversial, I feel you must know that and evaluate my analysis accordingly.

This is a complicated topic with no simple answer. Anyone who thinks the answer is simple (e.g., they either were or weren't) is trying to sell you something one way or another.

There are many posts on here on this question. Searching for the term "Hasegawa" will come up with many of them. See e.g. this post I wrote awhile back.