1. If you send the DSP-122 form to KCC, you are guaranteed to receive the 2nd letter in about a month regardless of when you pay the $375 fee. The 2nd letter will pretty much confirm your intent to do AOS and will remind you to pay that $375 diversity fee. You should pay that fee well before shipping your AOS package to Chicago Lockbox (when your number is current) because you will need to include its receipt in your AOS package.
2. I also had the same concern. I call USCIS and they said as long as you are in the US in legal status, you can do AOS. I'm on F-1 too doing my master. And previous F-1 dv lottery winners successfully adjusted their status without any problem.
3. Some people have posted their interview experience in the previous years' AOS threads. As far as know, it's a friendly, short, and easy interview. You won't have any problem with it if your profile is clean.
Thanks for the answer.
Let's hope we can get the GC ^^
By the way, when you list the educational information in Form DSP-122, did you list all of your education, I mean from kindergarten? I think that's a little too much don't you think?
Thanks
keepkeep