If I get payment for my own game and have some $ on my Gross Revenue, can I just use it to directly buy a game from other creator? Or do I have to make payout to my bank/PayPayl account and use it to buy game from other creator? Or can I pay with directly for some service from itch.io, like advertising or something?

To use the money you have in Itch, you must first complete a withdrawal process that will transfer it to PayPal or Payoneer (depending on your choice), and only then can you use it to buy something in Itch.

No.

There are many legal reasons for that. One of them is money laundering. Refunds. Taxes. And so on.

It sure would by handy to buy assets and have correct paperwork automatically. You need to realize that you are technically a business if you sell. That's why you have to do a tax interview. And businesses do not buy games for fun. But they do buy assets.

Itch does not offer services that I know of. If you want to support Itch, slide the revenue share slider to be higher than 10%.