1) Wait at least a week, a whole month isnt required.
2) No, you will still get a statement that posts.
3) You can pick original payment, or flight credit - So just pick flight credit, and apply it to your next trip. If it gets refunded to original payment, chase will eventually send you a check, but it takes a few months.
4) Not totally needed. But also if it makes you feel better why not. You dont lose anything. I use a SW giftcard I bought at a discount to pay for my CP fees. This is the time of year you can find some good deals on SW GC.

If you think you might want to try to Qualify for CP in 27, for 27 and 28, maybe consider the chase business card instead. Then you can save your personal signup for the end of next year, and couple it with a second business card. Also you can signup for the business card without canceling the Premier, and keep it until your annual fee is due(wait to cancel until after AF hits, so you get your yearly RR bonus).