What is exacting bitcoin mechanics have for preventing faking bitcoin?
in the physical Money such as Dollar banknotes have some protection mechanism such as Type of paper and ...  (related link: https://www.wikihow.com/Detect-Counterfeit-US-Money)

P.S. I have read electronic coin definition in bitcoin white paper but I need a real example of this concept something more clearer and more understandable

Is the possibility of discovering private keys with random testing by considering the increasing number of e-wallet?
what the prevention solution in cryptocurrency such as bitcoin is? Is there any mechanism such as "I am not a Robot" (Captcha) or blocking the user with the iterative wrong private key?

What mechanism for proof unique public key when creating a wallet happen with several sources(such as "wallet.btc.com" ,"wallet.bitcoin.com", "www.blockchain.com/wallet" and... )?

How to prove it different generating e-wallet website(such as "https://walletgenerator.net/" and  "https://www.bitaddress.org/" ) doesn't create the same e-wallet(With similar specifications)?