I recently had the same sort of issue with my Motorola z mobile, battery turned to junk.
Severe drops like yours above and it would even turn off and not turn back on unless connected to a charger. When I connected it tho the battery had read as high as 60%.
Returned it to Motorola, they claimed it was the battery and replaced it. But e en after repair it continued to show problems.
Ended up having them refund me, how long have you had it ?