Let's say I save the private seed of my Exodus wallet, how can I be sure that in 20 years from now, Exodus wallet will still be a working product, that I can download from a new computer perhaps and import my seed into?
You can't be sure that anything will work 20 years from now, and mostly likely Exodus and most of the stuff you have now won't work.
If you look back in past there are already some bitcoin wallets that are not existing anymore, like Multibit or many old ledger devices.
This is not the problem for Bitcoin as long as you have seed words or private keys in safe place, you can always recover it and use any wallet available in future.
The private key of my Bitcoin wallet is different ofcourse, but I do wonder, will this private key allow me to import the address into other wallet softwares? Or do I have to import it on Exodus?
Don't speculate and try it right now, you can even create new test wallets and see if it works, and it should work just fine.
You can have multiple addresses formats in many wallets (Electrum for example) and bc1 format is currently best one you can use.