Congratulations, that is a very nice bike. I ride one daily ('82, 58 cm). Chombi has one he's owned from new. It is a somewhat flexible frame but mine rides very nicely, very comfortable and I've taken it on five centuries so far in addition to the daily commute. Mine has a shimmy which I haven't solved yet, interested to know if yours does?
Hub, BB, headset bearings should be disassembled, cleaned, regreased, adjusted. That might take care of the chirp but anyway should be done, as the current grease could be 40 years old. Shifting issue could just be limit adjustment on front derailleur. Check chain for wear, a new one is just $10. Shop should check tension on the wheels but with luck it'll be fine.
Respected and mustachioed forum member noglider is now supervising the wrenches at a bike shop in NYC, if you don't have a regular shop you might find his.
No shimmy after a couple months of riding this thing. Bombed a hill at 40mph the other day and didn't experience anything scary either.