It sounds like the head unit and its Bluetooth functions have suffered a pretty major electronic failure. The good news is that you can replace the head unit for reasonable money these days, and get a better unit with more features into the bargain.

But before you rush out and replace the unit, try to find the reset button (often a small hole into which you poke a probe) to effect what is basically an Ctrl-Alt-Del reset. This will sometimes restore the unit to full functionality, so it’s definitely worth a try. You could also try disconnecting the car’s battery overnight to see if that resets things.

Any vehicle of this age has to be approached on an individual basis. It’s likely to have covered a lot of kilometres by now, so any major (or minor) component could be well past its best.

Any Subaru transmission that doesn’t shift properly or is slow to engage a gear or shudders under acceleration needs to be either investigated further or avoided completely. Don’t forget that the Liberty was all-wheel-drive, so that places extra strain on the transmission as well as making for a more complex arrangement if it does need to be repaired or replaced.

In high-performance Subarus (such as the WRX) the transmission was something of a fuse if the driver got a bit over-enthusiastic, but in models like the Liberty, the four-speed automatic was a sound unit. When test driving the vehicle, make sure there are no thumps or vibrations when the gearbox shifts down, and try to shift gears manually. The gearbox should respond instantly to manual input, without any hesitation or noise.

I would use the factory recommended oil, at least while the car is under warranty. Once the warranty has expired you could use the Mobil oil and shouldn’t experience any problems.