Let me refine the question a bit lol. Can I use any exchange that I have BTC and ETC on and The hardware wallet supports BTC and ETC?
when I give my crypto exchange my public address of my wallet to do a transfer , does the exchange know from the address any info like the wallet I am using....or?
Even with the refining, I still do not understand what you mean. There is no connection between hardware wallet and exchange, if you signup in exchange, they generate wallet address for you and you have no choice than to use that to make deposit in the exchange. If you want to make withdrawal from the exchange, you provide an address and the money is sent there. If the address you provided is a hardware, it really do not make any difference to the exchange, they will send your money there.