No, Bucky didn't kill the Starks in the comics.
Yes, he did. It was a significant plot point in the comics.
Yes, Bucky did kill Tony's parents in the comics.
Yes, Bucky did kill Tony Stark's parents in the comics.
The Starks' deaths in the comics were often a result of various complex plotlines and conflicts. Sometimes it was due to betrayal, while other times it was from powerful enemies.
Well, it depends on the specific comic series. In certain story arcs, Bucky is shown to have a role in that tragic event, but it's not a constant across all comics.
Bucky died in the comics due to a combination of challenging circumstances and powerful antagonists. It wasn't a straightforward event.
No, they didn't. Their relationship in the comics was more of a deep friendship and comradeship.
Batman typically adheres to a no-killing code, but there are rare exceptions in some darker or alternate comic universes where he has been shown to kill.
In the comics, Bucky didn't become Captain America. Captain America has mainly been associated with Steve Rogers. However, Bucky has had significant storylines and developments of his own.
Some comic storylines suggest that Bucky might have had a crush on Steve. It's not always explicitly stated but can be inferred from their interactions and the depth of their bond.