The sentence is difficult to parse because it has a long relative clause with no wh-word. In addition, the relative clause has an extra phrase in the middle. It may help to think about the sentence like this:
- The two men were Anton Voloshin and Igor Kornelyuk.
Now we may not know who these two men are. We could use a relative clause to explain this:
- The two men [who Savenko was convicted of helping to kill] were Anton Voloshin and Igor Kornelyuk.
This relative clause has a gap at the end. We understand the gap as referring to the two men. So the sentence can be modeled like this:
- The two men [who Savenko was convicted of helping to kill
them] were Anton Voloshin and Igor Kornelyuk.
We might want to give some extra information about Savenko. For example we could show that he was an Iraq war veteran:
- The two men who Savenko [an Iraq war veteran] was convicted of helping to kill were Anton Voloshin and Igor Kornelyuk.
In the Original example, the word who is missing. This is because we don't need to use who if it is not the Subject of the relative clause.
The Original Poster's second question
Savchenko, an Iraq war veteran, was convicted of helping to kill the two men Anton Voloshin and Igor Kornelyuk.
The sentence above gives us the same information as the original example. However, the information is arranged in a different way. In the original text, it sounds as if they already told us that Savachenko was convicted of killing two men. If we used the Original Poster's (OP's) sentence in this situation it would sound a bit odd. Compare these two pairs of sentences.
Savenko was convicted yesterday of helping to kill two men. Savchenko, an Iraq war veteran, was convicted of helping to kill the two men Anton Voloshin and Igor Kornelyuk.
Savenko was convicted yesterday of helping to kill two men. The two men who Savenko, an Iraq war veteran, was convicted of helping to kill were Anton Voloshin and Igor Kornelyuk.
The second pair is better, because it makes the two men from the first sentence into the Subject of the second sentence. We like to organise our writing like this. In the first pair of sentences, the second sentence seems to be too similar to the first one.