The kucoin account is registered to my official e-mail addres. Do i need to use monero mixer? Which monero mixers accept small amounts of this coin (eg $10). What are the anonymous ways to transfer Monero to my wallet? I will be very grateful for the answer.
After an exchange sends you the XMR, they will have no clue what or whether you done anything with your coins, since every transaction is being built with your output (you got from the exchange) and currently 15 decoys. So if your outputs occurs in a transaction, there is a 1/16 chance it was the real spend.
But exchange will know your XMR address belongs or associated to you. So in case if you share same address somewhere else (like on this site) the exchange owner will know that's you or associated to you.
You don't need and shouldn't use any mixers, since there is a high probability they simply try to scam you, since Monero doesn't need mixers to be private per default.
The only exception is when you send funds from an axchange to Alice and Alice sends them to the same exchange again, the exchange can obviously expect them to be those they sent to you if the amount (minus fees) matches your withdrawal.
NO! The exchange will know all the info you entered. If they wanted, or had to, they could share that info with whomever. The only way I know to make that transaction hidden is after you sent it, send it to another wallet. Then send it to yet another wallet, in different amounts.
Some people send it, in different amounts and same amounts, to 3 different wallets consecutively.