Apple "13 2011 MacBook Pro touchpad battery faulty issue. (10.13.6 software problem)
The most likely cause is that the “tech” broke the trackpad when they removed the battery, so the Mac is looking for a Bluetooth trackpad instead. (Or at least, they 'loosened' it sufficiently that it has subsequently broken.)
Frankly, your school has given you a 10-year-old laptop, with no battery, and a broken trackpad. (And a startup disk called &quot;aaaaaa&quot;.) Because there's no battery, the CPU performance will be throttled at best.
At worst, the power adapter can’t supply enough current at all times to even make the OS stable. Let's hope it doesn't have the original hard drive....
Take it back to them, and tell them it's unreliable. This is not a software problem. You need hardware service on this unit or a new Mac.