Hey guys! How is it working: I have 1 eth on binance and want to withdraw it to my personal wallet. And I exactly receive 1 eth, no fees are charged. How binance is doing that? Is some smart contract used?

You can see some info from bscscan. Search for your address and go from there.

How is that related if initially I deposited eth and withdrawing eth?

I mean why and how there can bsc chain be used?

Binance is a cex

They make the transaction, not you

They decide how mucb you'll get and how much fee should be charged

But I mean I want to deposit the amount like 5$ to binance with transfer fees of 10$. I need to pay 15$ in eth in general.

They generate for me some empty eth address where I should send my 5$. Now there is only 5$. And then I gonna withdraw it to my wallet. I should receive 5$. But transfer fee is 10$. But binance does allow doing it. Does it mean I will receive 0$ in my transaction?
How it works?

They will probably show you that "we will substract this much as fees" while withdrawing