MDBT42 crashes after about 1 week

Vin/GND is perfect, so yes, lets see if the battery helps.

I've found during testing that if say I had my phone connected to the device and then tried to connect to the device that it wouldn't even display as an option to connect to.

Yes, this is what you'd expect.

If you had any other way to display information (eg soldering a LED onto some other pins) so you can see if the code is actually running or not that could be really handy.

If you were to modify the code to save everything to nonvolatile storage then you could also just enable the watchdog timer, which would make 100% sure the device could never crash (not that it should anyway).