Is it possible for the communists to take control of Germany instead of the Fascists in the 20s/30s?]
It's possible, and something that I've been toying with for my alternate history "Petrograd, The Red Flame of Russia."
I think that by 1932 it was rather late for the German Communist Party to seize power through elections, seeing as to how the German C.P. only won 14.3 percent of the voted in the 1932 elections (up slightly from 10.6 percent in 1928).
In contrast 33.1 percent of voters voted for the Nazi Party during the 1932 elections. (source: The 12-Year Reich: A Social History Of Nazi Germany 1933-1945)
However, a major problem for the German C.P. was Stalin's stubborn insistence that the communists should not see the Nazis, but the Social-Democrats as the main threat to a successful revolution in Germany.
Trotsky may have not made the same mistakes as Stalin concerning foreign policy towards the German communists.
Being as he was a different person with (very) different views I'm assuming for the sake of alternate history that he doesn't bungle Germany by allowing it to fall electorally to the Nazis.
The question remains by 1932 for the German communists: seeing as to how they can't win power electorally (being as they were far down the list votes-wise) and, realizing the threat posed by Nazi Party paramilitary Storm Troopers, what should they do?
The Nazi's victory being almost assured in the 1932 elections (their electoral success partially the result of backing from businesses), what to do?
Which is why I think that a communist triumph in Germany in 1932 is a very poor choice for a POD.
The only way that the communists could have seized power was through illegitimate means, i.e. through force.
Assuming that Trotsky is in charge in the Soviet Union, a policy-shift different from Stalin's would and could have taken place. The Nazis, and not the Social-Democrats, could very well be stressed by Moscow as being the bigger threat to a German revolution.
Emphasis could be put on an insurrection waged in the streets of Berlin rather then on a slim hope of an electoral victory. Perhaps the Alliance of Red Front Fighters could seize power militarily.
Assuming that this succeeds, I'm assuming that the Nazi Party would be banned, as well as any other significant opposition parties. In effect Germany would become similar to the USSR, i.e. as single-party socialist state.
Another earlier attempt at revolution could very well happen in 1923, but even then it's a stretch, but maybe not as a great a stretch as the communists winning power in 1932 electorally.
My bets are on the dates 1923 and/or 1932, but not before or after. Past 1933 a German revolution is impossible, the German C.P. having been banned by the victorious Nazi Party in 1933 which took steps to make its rule permanent.
The other method to have a successful German "revolution" is to have the Red Army march into Berlin as in OTL, but that hardly counts as a true revolution as it did not originate domestically and in fact was exported by the Soviets like in OTL.
Furthermore I think it is unlikely that a successful German Revolution could occur in 1918-19, the German soviets themselves losing power historically to a German Constituent Assembly. (Which is a major reason why the OTL Bolsheviks closed their own Constituent Assembly in 1918)
Barring the dissolution of the German Constituent Assembly, German soviet power in 1919 is unlikely.