PedroR

You don't need to take the money? I don't know how do you think this works but I don't think you make the rules regarding this matter. If you want to risk it and not showing any money it's your decision, we are just informing you of what they ask on every interview.
Good luck.

There is no deadline, other than having enough time for KCC to process it before either the fiscal year ends or visas run out (which if it happens would almost certainly be in Sept anyway). Even if you "miss" your interview month and only send in your form after you are current, they will just schedule you into the next round once your forms have been processed.
With an estimated May interview date, as long as your forms are in by February you will probably be fine, to be ultra sure if they are in by Jan they should certainly have more than enough time to process them and schedule. Usual processing times are around a month but at peak return times they can take 2 months (this is usually around the time that the bulk of DV forms are sent back ie May-Jul/Aug) and then another approx 2 months lead to the interview schedule. (I suspect that with forms now electronically submitted the processing time will be cut, imagine the time actually involved in sifting through multiple tens of thousands of envelopes, moving them from reception to the correct desks internally, slitting them open, piling the pages into the correct trays etc...)

You don't need the documents for filling in the form. You will need them for the interview. Please read the instructions for selectees (.link from your notification letter) carefully.Interviews are based on case number order. Your case number is absolutely fine, I'm not an expert on EU numbers re estimating month of interview, but it is very safe.
You can fill in your DS now, or wait till you have married. If you fill it in now you will need to update it when you get married. Bear in mind you will need to fill in DS260 for your wife as well when she is your wife.
As mentioned they will be on high alert for "green card marriages". Be sure to take proof of a bona fide relationship along to the interview. Lots of info on this if you do a search.
Oh and congrats on both the selection and the future marriage!

The first question I think it is just the form but others will chime in the proof are needed for the interview. You are called in order of your case number the last numbers being the most important. Each area has it's own cut offs. If you marry before your interview your wife will come with you IF you can prove that you have a valid relationship some fraudsters marry to bring a friend over and that causes no one to travel. You look at the months visa bulletin to see the cut offs but your year doesn't start until October. All visas for that year must be issued by the end of the following year.