But I believe I don't need to enter my seed though into the nano ledger right?
Your hardware wallet is already set up, so no. You will only need your seed if the device resets itself during the firmware upgrade which has happened to some people.
I know the first thing I need to do is download ledger live. Then check to make sure the download hash file is correct. But there still hasn't been a case where the hash file was wrong right?
The building I live in was constructed about 15 years ago. In all this time,
there still hasn't been a case where a tenant got electrocuted by using a hairdryer in the bathtub. Nevertheless, I still don't allow my kid to bring a hairdryer into the bathtub. Do you understand? Shit doesn't happen before shit happens. When it does, what do the stats and previous history matter? Learn to do things properly or suffer the consequences.
After that, I need to create a new password right on ledger live?
I am not sure, I never had to reinstall LL on a different computer. But I assume you need to create a new account and use your existing or a brand-new password.
Do I connect my nano ledger so to it? Or do I add accounts first?
You need the Nano S connected so that it can be scanned when the accounts are being added. If you have funds on nested segwit and native segwit accounts, you need to add those separately. Sane thing for Legacy.
Then only this, do I go and update the firmware?
The order doesn't matter.
When you open the ledger live program, you need to create a new password before you connect the nano ledger s to it right?
Just try it for God's sake. Nothing is going to happen.