Yes you can buy and sell options the same day, just like all other securities the purchase must be paid in full and you can not use the proceeds of the sale to cover the purchase
There is no rule that states you must have $25,000 in your account at all times - you'reconfused with the pattern trader rule which states you must have $25,000 in equity in your account at all times - there is a BIG difference bewteen maintaining equity of $25,000 and having a balance of 25,000 -
Also the pattern trading rule states you must have a margin account - options can not be used for margin since they have no loan value
To answer your questions - yes you can buy and sell the same day and you DO NOT need $25,000 in your account at all times
You can but not for free
Yes You can
Does option day trading require you to have 25k in your account at all times?