One thing to consider is Graphene and Calyx both say they are designed to work on Google Pixel phones. If you have a different kind of phone you should search on your phone model and see if anyone has installed those on it and how it went for them.
Other than that, they are basically just de-googled Android so I would expect the things you mentioned to work. You can get many apps from Fdroid or use the Aurora client to get them anonymously from the Google store, though I don’t know for sure if that works in all circumstances. My brother uses Calyx and I know he has been able to install at least one proprietary app (for his car) and I think one from an insurance company or something like that.
edit: update, I just checked the CalyxOS site and it says they also support Motorola moto and the Fairphone.