Yes, if you update an app in a profile (doesn't matter if it's the Owner, private space or secondary) the app gets updated everywhere else you have also installed it.
As for your second question, apps do need a way to update, whether that's through Obtainium, Play Store, Fdroid etc (unless of course if it has an auto-update feature built into the app). If you have installed the app in the secondary profile, and have a way to update it, then you don't have to keep the app in the Owner profile; apps can update in secondary profiles and push those updates to other profiles as well.
I actually installed Google play services in my private space, download those apps apk via SDMaid/split apk merge and install the app on my owner profile. When I update my app via the private space store, it updates my app in my Owner profile.