So, regarding the account: it depends. AFAIK, there's no "graphene account" in grapheneos, but you can use the regular google account after installing sandboxed play services. Note: you don't have to, the only things from google I personally used were gcam (since their hdr+ thingy is quite good) and photos (since foss alternatives I've tried can't 3d transform), both without play services and internet access. On other roms there may be an optional account (ex, /e/os).
Applications: there's a messaging app (regular SMS) and gallery (not sure here, tho, mb there wasn't; once again I decided to keep using google photos), otherwise - nope. All can be obtained from f-droid/play store/aurora. Syncing probably needs to be done via 3rd party stuff (I'd probably go with self-hosted nextcloud instance, which can be done rather easily and for free with tailscale if you have a spare laptop/pc)
App installation: I personally went with f-droid plus aurora (since the proprietary software I use doesn't rely on play services other than for sending notifications, exception - gcam, but fixable with gcam services provider from f-droid with the caveat of not being able to use sandboxed play services due to the name collision). Idk how exactly sandboxed play services are "better" compared to f-droid, mb in terms of software availability? Otherwise I prefer f-droid since stuff there is Foss, trackerless and overall better audited (paste here the links to numerous articles about actual malware being found in play store).
Self-hosting nextcloud is relatively easy (I can drop some links later if you're interested), but you can also keep using whatever you used before. Also (correct me if I'm wrong) /e/ provides their cloud with some amount of free storage, so you may want to start with that.