Your answers are enough for me to be enlightened and finally feel at ease with my seed alone. This question has been bugging me for some time. Thanks to both of you!

As long as you bought your ledger from an official source, the seed is all you need.
Yeah, I got mine from the official site of Ledger.
With hardware wallets like Ledger you don't have access to your private keys and they never leave the safe environment of your device.
You have your seed words. Even if you connect your Ledger to Electrum you still can't see your private keys. You don't need them if you are using a Ledger HW. Just make sure your seed is kept away from prying eyes and never store or enter it anywhere online.
Got it! I was thinking that the golden rule "If you don't own the private keys to your coins, you don't own them." applies to all wallets.
One private key unlocks access to one address. You can have X number of addresses. The seed unlocks access to every single address generated in your Ledger Live.
I'm sorry. I got the OP wrong. It should be private key to my address and not to my wallet.