First things first … Did you contactsupport ? With all this trouble there should have been something they could do for you.
Anyway …
For reboots see the rebootsguide.
Not receiving calls or texts is not always down to the phone, there are provider issues sometimes, and a new SIM card has occasionally resolved issues if in doubt (there’s trouble with older SIM cards to be found in this forum).
You could check with a preferably newer SIM card of a relative or a friend, whether the SIM card plays a role in this.
Else … there’s the interactive Fairphone Troubleshooter.
The first easy measure with a slow phone would be to turn it off and on again.
A more drastic measure would be backing up all the important data from the phone and then doing a factory reset, which would delete all user-related Apps and data, leaving only the OS and the recovery tool on the phone.
Furthermore … If the OS installation could have become somehow faulty, the phone could be completely wiped and installed from scratch.
If you happen to have fairphoneangels in your vicinity, they could perhaps assist you with any of this.
If you still are on your first battery, please make sure it isn’t the battery that gets so hot.
Even if it isn’t, keep in mind batteries don’t last forever. Warranty on them is 1 year.
If you happen to have fairphoneangels in your vicinity, they could perhaps help you determining a possible hardware culprit by swapping parts (e.g. the bottom module for charging problems).
As mentioned, a factory reset or reinstalling the current OS might already help for software matters.
Or perhaps there are simply some updates missing?
What exactly does it say in Settings - About phone - Build number?
But your general idea is valid. New OS versions tend to sort out older problems (while mostly introducing new ones especially in the beginning 
).
Fairphone are indeed currently preparing an upgrade from Android 6 to Android 7 for their Fairphone OS and Fairphone Open OS, due soon (hopefully).
But this would not be the only option. The Fairphone 2 is very open for installing different OSes.
A lot of users here like to use an alternative Android called LineageOS, which on the Fairphone 2 is based on Android 7 since last year already and currently undergoes testing for being based on Android 8. If needed, LineageOS can be outfitted with all the Google Apps included in Fairphone OS, too.