"[W]" is what you are supposed to do when you are quoting something starting in mid-sentence.
Probably was something like "Ramble ramble ramble ramble, but when Barack Obama was […]".
https://en.wikipedia.org/wiki/Bracket#Square_brackets
No.
[sic] is for when there is a grammatical or spelling error that is being left in intentionally for context or another specific reason, so that it is clear that it is the quoted person who made the error and not the person who is quoting.