Reddit mentions of Mainstream Engineering QT2000 QwikCheck Acid Test Kit

Regarding whether the system was properly installed, you can buy yourself one of these: https://www.amazon.com/Qwikcheck-2-Second-Acid-Test-Kit/dp/B00CD70Z12

And watch this video: https://www.youtube.com/watch?v=zY2GzCsxKJY

If there's acid in the system (possible/probable by the sounds of it?), there's your problem, and your proof that the techs aren't competent.

As far as proving whether they changed out the compressor, there should be a manufacture date encoded on the label. If it's after the date the system was installed, it was at least replaced once. The trouble is going to be reading the sticker on the compressor. You're looking for the smooth black cylinder about the size of a loaf of bread (compressor) down at the bottom of the big fan thing outside (condenser). You can try taking some pictures through the slots at the top and we can see if anyone can read/decode them. If you're handy, you can remove the screws holding the top/fan on and carefully move that aside to get a camera down there. If you do this, first pull the disconnect switch on the side of the house going to the condenser and be very careful not to damage the fins or wiring to the fan. An able-bodied helper is recommended to hold the top assembly while you reach in with the camera.

PS - Not a bad idea to ask any technician for the 'old parts' when getting any kind of work done (on your car, house, whatever). Just remember if you do that you also take responsibility for disposing of the old part. Depending on what it is and where you live you might have to pay someone to take it. In the case of an old compressor that shouldn't be a problem.