Yes Tete, I remember when you got this bike. I don't remember all the details but I do remember you've been one of the best students I've ever known. Unlike many we see here you have the guts to hang with it. It's not easy I know.
At any where from 90K to 120K these bikes are well worn and many of them are in need of extensive rebuilding. There's a guy here with 250K on an original Airhead motor and everybody else thinks they will do the same. Thatr is rare. It's so rare I actually don't believe him. I'm not calling him a lier but it's either that or he has made a mistake in his records.
Start running BMW Brand 20W-50 Dinosaur (not Synthetic) motor oil. Do not even think about the promises of a New World Order where machines run forever on piss made by the Gods of Capitalism. If you can't get BMW brand motor oil, usually only available at BMW dealers, then use Spectro (they make BMW oil).
I think you should buy a compression gauge. Get a used one from Ebay. I bought one 6 months ago for less than $20. One of the cheaper push in types work fine on Airheads, the screw in type are more expensive and if you are buying used the threads may be messed up.
Here is what looks like a good deal. It also has screw in but it has push in. If any of the adapters are messed up they may be available. The rubber tips look good. And it has the original box.
Start saving your nickles and dimes. These are great bikes and they are usually cheap to start with but they will need work to keep running. Most of us have much more into these bikes than they are worth.