PAU1,
Phew! An awful lot of questions in one post, no worries though, will take a stab at answering them:
A1. For anyone doing AOS, the $330 DV administrative fee has to be paid ahead of time. So you may go ahead and make the payment now, or you could wait until you're certain as to when your CN will become current and then make the payment.
A2. Correct, you do not need forms I-765 and I-130
A3. Option "H" and be sure to type in "DV Selectee Notification Letter Included" in the section in front of that option.
A4. Yes.
A5.1: No document required if you have no criminal past
A5.2: No, PCC is not required for AOS
A5.3: Highly advisable to still have your high school diploma handy, in addition to your BS and PhD documents. Some IOs have insisted on seeing the HS Diploma in the past. Doesn't hurt to equally have an employment letter as part of the supporting document.
A5.3(i): Please see the following link for required documents and additional information regarding the DV AOS process (the spreadsheet has about 6 0r 7 tabs with useful information on them):
https://docs.google.com/spreadsheet/ccc?key=0AozhLxh12qzYdDU3WkxHaFFtdVI4Y01oTFc3ZnZlb1E#gid=1
A5.4: See A5.3 above.