I used to have a partly similar problem: very long time to start the phone and problems when starting, process system not responding and, after a few weeks, the phone not starting at all any more (it got stuck at the “Fairphone” screen)
More or less similar problems are described in other topics, like here and there.
For me, this meant I had to do a hard reset of the phone around once every month to get the phone running again.
I sent it to repair twice, but this did not really solve the problem. However, since the last reset I didn’t reinstall some apps I didn’t use very often and some other apps of which I presumed they could use a lot of memory. This seemed to work: my phone has not died for almost 2 months now!
I never experienced the Playstore problem, however. And I don’t use any bluetooth. So I can not really be sure this is the same problem.