You can install almost any app (for example I can't install the eBay app as it isn't shown for my device in Playstore and when you want to install it from the Play store website it says installation is not allowed for my device).
Bluetooth connectivity is a matter of Hardware. If it works good on stock OS, it will work on any other OS too.
You will basically see no big difference to stock OS in daily use, except for there is no AI. And you can't use payment via Google pay.
The stock messaging app for SMS is very basic, it's doing the job and that's it.
Besides that you can install any messenger you wish, whether it's Signal or Whatsapp etc.
You mentioned telegram, which isn't a privacy messenger at all. I would not recommend to use that if concerned about privacy.
GrapheneOS can't make apps more private when their design or purpose is made to be the opposite. The apps act more or less the same way they do on stock. If they aren't privacy oriented on stock, they won't magically be it on any other OS.