First, your fiancée needs DS-160 (not DS-260 mentioned in your message) and the Embassy there should be the one, when she is actually going to have her interview. So you would need a new DS-160 for Warsaw.
1. Kazakhstan or Turkey won't agree to take your case without a residency. The best and the fastest option is to apply for schengen.
2. With K1 it's better to pick the interview date and then to apply for schengen visa. You can reschedule the interview appointment up to 3 times in Warsaw without additional fee. You can book the appointment ($265) even without an eligibility letter from Warsaw.
3. Your fiancée (or petitioner sometimes) should receive said eligibility letter in 5-6 weeks (on average) after the notification from NVC.
4. There will be no account on CEAC and no invoice number for K1. K1 doesn't acquire uploading anything. You bring all documents to the interview.
5. If your fiancee's interview will be in Warsaw, the medical can be done in Moscow, Minsk, Warsaw, Krakov and before the interview.
It's faster and cheaper in Warsaw in comparison to Moscow, but in general the process depends on the age of an applicant. So in she is younger than 25, she would need additional 3 days in schengen area before the interview, and that might be inconvenient in case of extremely short-term schengen visa. If older than 25 you can receive the results the same day in Warsaw.