Apple "13 2011 MacBook Pro touchpad battery faulty issue. (10.13.6 software problem)

Recently, my school that gave me that laptop asked it back, and it removed the battery. I'm forced to use the charger but that is not the question right now.
I currently need help because it doesn't actually show the settings in the trackpad settings, instead it thinks i'm using an iMac because it has bluetooth trackpad + keyboard connection.
The issue and the pictures:

You might see this kind of a post alot now, it's an issue on high sierra. I recently re-installed it because of performance slow-down, actually that is not the thing i'm talking about right now.
I currently have no other idea other than downgrading to 10.12 sierra

Any ideas how to fix the trackpad?

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 "aaaaaa".) 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.