1. You are a green card holder, so writing any of LPR, Green card, ARC, or I-551 is fine.
2. Exact date not necessary. Just take an approximate guess. They're not going to penalize you if your actual date is different.
3. Download the I-131 instructions.
4. Anywhere from a month to 6 months after you give fingerprints.
5. You need to give your US address on page 1, but on page 2 you can specify the US consulate where you want to pick up the permit.