It's the same relationship between the branches of a tree and the seed you put in the earth that grows into that tree.
We have a seed that can be used to derive child branches and child keys which makes the relationship is one directional (you can always derive the child key by having the seed but you can't compute the seed from the child key).
Take a look ...
Sadly if you lost your seed phrase (12 or 24 words) you won't be able to regenerate your private key and get your funds control back. Best advice, look harder where you wrote it or stored it.
PS. Never write your seed phrase in any online place or take any picture, just piece of paper very well stored.
If the private keys are visible to you on your AWS account, then they'd be visible to anyone who has your session tokens (i.e. if a hacker would simply need to take your cookies to view the keys). So it's not only the cloud provider you'd need to worry about.
Always best to sign transactions on your own node which has no connection to your online accounts. ...
generally speaking the answer is no: you should generate every public address to check it's balance and the possible addresses are too many to be checked all.
in your case, if you remember the wallets where you imported the keys, you can only check the derivation paths used by them.
even the addresses that can be generated from the first branch of the ...