From my basic understanding of Exodus and similar apps... (someone more elite than I can chime in with corrections)
A wallet is automatically created for you when you open Exodus. A wallet, technically, is not where you are sending/receiving your crypto. A wallet is more like a container or warehouse for...
Addresses! These are the things that you can send and receive crypto with. If you want to see the address for your cryptocurrency of your choice, click on that currency's icon in your portfolio (exodus wallet) and choose receive. The address that displays is yours.
You can set those up to basically rotate, and create a new one for privacy sake, but just know that while difficult, it's far from impossible to link your accounts.
As for that 12 word seed phrase... Try going to Settings, and it's somewhere in the backup settings I think.
As far as buying Crypto... If you're just doing BTC, I feel like Moonpay is awful. It's so inconsistent and I hate it. I just do KYC at Cashapp, Venmo, etc and then send it to your Exodus address. Be warned, if you do larger amounts for CashApp, they flag "suspicious BTC addresses" and refuse to send the 2nd, 3rd or 4th time, but like I said you can set your wallet up to refresh its address as often as you want.
One last thing: don't use Cashapp, Venmo, etc to send crypto to a vendor. Most likely it will be blocked already because some doof already sent it this way, but with Cashapp, Venmo etc, you don't really hold your crypto. They do. Makes it easier to flag vendors but if the app you're using doesn't like you... they can just put a freeze on you, and your crypto may or may not see the light of day. Exodus is self-custody still I think, so there's less problems there.
Hope this helps.