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?
If the exchange supports the address you have given then you don't have any problem but from my time and experience I haven't not noticed any exchange that doesn't support such an address like yours, but it is best to be safe so yes I think your question is valid and to further your understanding you should also learn to do your research on things like this so you have a wider knowledge.