1. Oath ceremony applies to US citizenship, and not to GC. I'm confused.
2. What exact errors are you seeing? It's not uncommon for GC to take 6 months to arrive. Also, did you change US addresses since you applied for GC?
3. You don't have to wait for arrival of SS card. Fill out the SS-5 form, take it to the SSA office and get a SS card. You have a stamp in the passport proving your status.