fawkes,
I know this is an old question thread, but I'm sure the answer can benefit others:
The key with the phrases 'to the extent that', 'insofar as' and 'insomuch' isn't so much in picking the phrase that means the right thing. They all really mean the same thing and I doubt you'd ever have a GMAT question that asks you to choose between those three phrases. Rather, the key with these is to ensure you use the whole idiomatic phrase correctly. As such, you need to consider the entire phrases:
"To the extent THAT I'm aware, our team is winning."
"Insofar AS I know, our team is winning"
"Insomuch AS I know, our team is winning."
Grammatically, these three are correct. Wrong examples would include:
"To the extent AS I'm aware..."
"Insofar THAT I know..."
"Insomuch THAT I know..."
In summary: This is more of an idiom issue than a word choice issue.
Onto your second question:
'To the extent that propaganda may help to decrease youth violence in a poor country, it is probably not the result of restoring the youths’ faith in their country’s leadership.'
The antecedent of "it" here is the "propaganda." You can test pronouns by replacing the pronoun ("it") with the antecedent ("propaganda") and checking that it all still makes. In this case, it does.
Happy studying,
Brett