I never experienced that the Google account appeared for other logins, this will only happen if you are already signed in to a Google service within the used browser or maybe if you turned on to use your Google account for passwords, wallet etc. That's not graphene specific, it's the same on stock android too.
You can check this under settings where you see your accounts, you can disable there if the Google account is used for passwords etc.
I could guess it's turned on or was turned on, because you got this pop up to choose between proton and Google.
You also need to disable automatic password and personal data filling in the Browsers you use. I use proton too and it works pretty good most of the time. If it isn't working automatically, you can open it manually and copy and paste your data into a site or app.
Firefox or not is a personal choice. It has the same advantages and disadvantages it would have on stock android. Graphene can limit the access apps have, but it doesn't change the apps.
If it is mostly about ad blocking, vanadium and Brave do have an internal AdBlock Feature. If you want to block ads overall, you could use the dns entries from adguard, it's explained on their website and you don't need to have a subscription or install an app for this.
Profiles: Apps within the same profile can (but don't have too) communicate with each other. They can't communicate with apps in other profiles and if you close a profile all processes in this profile are stopped.
Keyboard: don't know what you mean with "idle". It's running in the background, it's a keyboard.
Pixel Camera: when it has no Internet connection it's safe (apps can send background data on mobile networks too, you have to disable this for every single app in the specific app settings in the apps section of graphene... that is where you can clear cache of apps and uninstall them).
But Pixel Camera fills in exif data like time, camera used etc. You would have to erase those manually if you don't want to share this before you send a picture.
Google Photos: without network connection it's safe. But for certain things like editing pictures it probably needs an Internet connection.
Graphenes own app store (you find it in the app drawer) has the app markup, which allows you basic editing like filters, cropping etc from within the standard gallery app. For basic needs it's good enough.