Congratulations! I hope youīll get many many nice miles out of your new Benz. Sounds like a nice set of wheels. I just bought my second and third Benz too, so I am not an expert here. But some things Iīve already learned and thanks to this board alone. Great people here!
The bouncing fuel gauge is the sensor in the tank. On my 300E (I havenīt had the chance to get my 560SEL shipped to my house yet so I havenīt studied it so closely), the sensor seems to be easy to access and replace from the top of the tank in the trunk. Just remove the cardboard/trim that covers the rear seats. I havenīt changed mine yet, but will soon. Mine bounces around from 1/3 or 1/4 tank.
Speakers... My W124 dash originally had 120mm units installed (flange measure). Thatīs about 4", but Iīve seen some 4.5" units too that could fit with a mm or two extra in there. I am planning to install a custom setup consisting of 4" in the dash and separate tweeters somewhere up front. The W126-series dash might room bigger speakers. I do not know.
The rear rooms 120mm too, enclosed in some plastic "cups" under the grille there. But it seems it can contain 140+mm units without any big modifications. I plan to keep the interior looking original. 140mm would be 5.25" or thereabout.
My car came with an aftermarket Sony unit, and I couldnīt see much special wiring for it actually. Thereīs an extra wire that might have been for the factory alarm to sense if the unit got removed. There are some instructions at MBCA.org I believe about removing the speakers and headunit. Check out the link from my W124 site...
As for the swaying in curves I am sure itīs related to shocks. I replace my rear shocks and the handling now is excellent. Floats through the streets and is glued to the curves.
Good luck! Search around the archives and youīll probably find much more infomation about your other problems too.