If your touchscreen is freezing, try a different charger. The touchscreens on many people’s Fairphone 2s have been intermittently unresponsive. See e.g.: Fairphone 2 unusable while charging
It was a big relief to me to realise that this problem only occurs when the phone is charging, and then to learn that it occurs only when certain chargers are used, as noted in the above list. Unplugging the phone or using a different charger (and then tapping the on/off button twice to refresh the screen) immediately restored full functionality.
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