From the sounds of it you may have a failing drive issue as well. But before you can address that you really need to get the battery issue fixed first. Once we see the CoconutBattery snapshot we can guide you on whats needed.
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=== Update (02/01/2019) ===
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You’er running on borrowed time! [https://support.apple.com/en-us/HT201585|Determine battery cycle count for Mac notebooks] You battery has a lifespan of only 1000 cycles you’ve exceeded that by almost 500!
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You’ll need to replace it first, here’s the needed part [product|IF108-063-2] and here’s the guide [guide|12340]
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When the battery gets to this level its power output is not stable which can cause instability like you are seeing.
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You should also rethink your usage pattern. You really don’t want to let the battery get to low before charging it up. Once you get down to 1/4 of the charge you tend to burn a cycle.
From the sounds of it you may have a failing drive issue as well. But before you can address that you really need to get the battery issue fixed first. Once we see the CoconutBattery snapshot we can guide you on whats needed.