1) My question is, let's say I have 1 BTC in my Ledger Nano S, and I plan to sell 0.2 BTC on exchange. So I send 0.2 BTC to say, Coinbase. Where will the remaining 0.8 BTC go? Will it stay in the same existing address in hardware wallet or will it store in another address in hardware wallet?
The remaining 0.8
BTC will be sent back to you.
2) I am currently using electrum mobile wallet to store my bitcoin. If I send all bitcoin from Electrum to my address in Ledger Nano S, will I see Bitcoin Gold and Bitcoin Diamond in my Ledger Nano wallet?
No. You would only send Bitcoins. To be able to recover and spend the other fork coins, you would need to import your Electrum wallet in a Bitcoin Gold/Bitcoin Diamond compatible wallet.
Regarding my 2nd question, if I send all my BTC balance to the address in my Ledger Nano S with a new seed. Then my electrum would have 0 BTC in it. So I import my electrum seed to other BCG and BCD compatible wallet, then I would still see those fork coins right even I have 0 BTC on that electrum seed?