Can I make SC, that register users and make some operations by just sending bnb to smart contract?

I.e. make user registration without metamask and web3, but just simple transfer BNB from user wallet to contract wallet?
It's possible if I just overwrite some method of eip20 (bep20) contract (maybe receive() method)?

Yes you can create a function that registers the details you want and then wrap the function inside receive so that whenever BNB is sent to the contract,that function is triggered.

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