- You don't need an account, and there is no such thing as a GrapheneOS account. Most of your apps should be able to be installed through either F-Droid, Obtainium, or the sandboxed Play Store. Some apps require Google Play Services, however, but LineageOS has an alternative called microG which works most of the time, and GrapheneOS containerises apps.
- GrapheneOS, I believe, uses the default gallery and SMS apps from stock Android; and they also have their own camera, PDF viewer, and web browser (Vanadium), which are developed in-house. However, cloud syncing and note-taking apps are not included. I would suggest either having a look on F-Droid, asking on this sublemmy, or checking out Privacy Guides to find some apps you'll like.
- GrapheneOS doesn't have a "cloud", as such. This is a good thing, and it lets you choose your own provider if you must. I would personally recommend Filen for files and photos, and Cryptee for notes.
- It is completely possible to use multiple app stores. If you use GrapheneOS, I would say use F-Droid or Obtainium when possible, and the Sandboxed Play Store for everything else.
- We like to use things like NextCloud because it gives us full control over our data, among other reasons. However, it is not essential. I, personally, use Filen for my cloud sync needs; but I also tend to use physical storage a lot because of my shitty internet and cheap hardware. You also don't necessarily need to pay for these services, but it's polite and it can improve your experience.
Good luck on your privacy journey, and don't hesitate to ask more questions. In addition to Lemmy, here are a few good resources:
I'm not entirely sure. I'm still using the free tier. A bit hypocritical for me to say that payment is polite, I know; but I do tend to use USB drives more than the cloud.