Yeah, Exodus is one of the more secure options out there - I also have it, if only because it was simply easier at first to keep multiple coins. Create backups as you note, and yes, you're able to export all your private keys for each wallet in there. Developer> assets> crypto> export private key
As far as I know Exodus is not an open source wallet, which basically means it can't be audited publically and checked for bugs. I hope that the team did their security audit well, but no one can be sure.
Ok, with open source software you still have bugs. Any software has bugs. It's just a question whom these bugs are found by.
May be most of the open source wallets no one checks. But the fact that they can be checked does make open source ones more secure. If you can't read the code yourself, but lets say have a ton of cryptos, you can hire your own security audit before using the wallet.
Saying all that, I wouldn't keep a significant amount of cryptos in anything that somehow connects to the internetz. For small change the incentive of a potential attacker is just too small to bother with stealing it. I keep small change on whatever wallets have the cleanest interface, as long as they allow me to export keys.