You probably should have the fuel filter replaced. What part of the country do you live in?
Welcome to the fun!
Agreed about the filter. Or, at the least, run a lot of Sea Foam carb cleaner though (2-3 tanks and, what the heck, ignore the instructions and toss the whole can in with each fill-up). If you don't have any stumbling issues, and idle is good (the "box of rocks" noise from the tranny is standard and no cause for alarm - I've seen a procedure to fix the one slightly loose bit, but that's a full tranny rebuild), I'd think more in terms of doing the plugs first. Typically I see 40-43 most of the time, with a slight drop with non-stop slabbing. 32 is certainly on the low side. AFAIK
, the only fix for the gauge is a new sender. But first, pull it and clean up any varnish that's developed over time.
Check the fuel line quick disconnects (allows removing the tank without a lot of fiddling with fuel lines). If they're the original plastic QD's, replace them like it happened yesterday. They're known to fail, with the male bit shearing off. The risk is anywhere from instant "out of gas' to spilled gas on a hot exhaust pipe. 'Nuff said. Pirate's Lair, Bimmer Boneyard should have the replacement metal QD's on hand. Look through the opening on the right side and you should be able to see at least one of the QD's. The original QD's are white plastic. BMW issued a tech bulletin on these but doesn't seem to have been aggressive about it. Bad them... >:(
Having stainless brake lines is nice (IMHO, not really necessary) but there's still rubber inside the stainless. If the lines went on when the bike was still new, I'd be slightly suspicious of them. Dry rot is really ozone damage and ozone is everywhere in the air. It's something to worry about when you have nothing else to do. :)
The throttle thing. First, it is a real thing. It's used to calibrate the ECU (engine control unit - computer) to the TPS (throttle position switch). Turn the key on and roll the throttle from fully close to wide open and back three times, and you're done. No need to scream through turning or be slow as molasses, just roll the grip. However, it's highly unlikely this will affect mileage. It will only change how the throttle responds near the closed end of the throttle motion.
Think about the plugs and carb cleaner first. And replacing the air filter might help.
On fluids, having a regular brake drain and refill is a good thing. I'd do the same for the coolant, too.
There are just OK copies of the BMW manual floating around on the Internet. Get the Clymer manual anyway.