You'll need copies of bank statements with proof of funds as required for the Non-O you will be applying for. Is it retirement or marriage? Check the Embassy for their specific requirements.
The title of the 60 day extension is "Visit Thai Family" so as long as you are legally recognised as the father yes you can but she must be with you when you apply
yes you do, the 800k for the first 3 months and never below 400k for the rest of the year are the conditions that the first extension was granted, fail to meet these conditions then your next extension will be denied [and technically you have been on overstay].
not in the first year (unless it's the income affidavit) and the 65k transfers can be used for the second year but has to be done in parallel with the 800k to 500k bank balances