Have you checked whether the battery has any deformities? See the battery guide about spin tests to test for this. If your battery is deformed (bloated), please don’t use it and contact support first.
This is probably testing mode (or factory mode). It can be activated by holding the volume down button while starting the phone. There is a clear eMMC option which reformats the phone, though it should leave Fairphone OS intact (i.e. it is similar to a hard reset).
But you can still access the recovery menu? If you can reach that, performing a hard reset may help. This will erase any data you have on the phone that isn’t backed-up elsewhere. Also, if you can reach recovery, it should be possible to charge the phone when in the menu, though I’m not 100% sure about that. In any case, before starting a hard reset, it would be good to have a sufficiently charged battery.