First, congrats on your successful transaction from exchange to your Ledger.
I think @Alexd1985 already explained & answered the whole thing. But let me answer question no.2 → “You just need to install Daedalus again in your new PC. And then paired your Ledger Nano S again. Your ADA will still be there.”
Don’t forget to delegate/stake your ADA, to get 5-5,5% reward. See this article below: