1. "Il faudrait" is the conditional form of "il faut".
The "il" is often ommited in colloquial speech. Your guessed it, it means "you should" or "you'd better".
2. Yes it is subjunctive. In English it remains the same "You'd better forget her/him."
3. The l' is the elision of "le" or "la", both elide to l'. Context makes clear which one it is. Since oublier starts with a vowel, you can't say "Faudrait que tu la oublies/le oublies."