I haven't spent too much in parts in owning my 2002 325ci, but I do most of the work myself (mechanical/electrical engineer).
1. Yes, it's likely that one or more of your bushings are shot. It would be best to replace your control arms with Meyle HD arms and bushings. Also could be your sway bar bushings as you said. For sure your FCABs if they haven't been replaced in a while.
Also, get an alignment.
2. Vacuum leaks are likely, especially the intake elbow. It tends to crack and degrade after 100K/6yrs.
Another possibility is one I just had, which is the fuel pump. The engine had a hesitation under acceleration for a while, then it started to fluctuate and stall before completely dying. I would recommend replacing it for under $200 yourself. It's pretty easy.
Vanos usually only causes a loss of performance. Other idle problems could be a busted DISA idle control valve.
3. Sounds like you have your stock diff. At 120kph you should be doing 3500rpm.
I do about 3200rpm at the same speed with my 3.15 diff. I really wish I had a 6th gear for hwy efficiency.
If you do plan to keep it a while, and the previous owners didn't take good care of it, there will be lots of maintenance to do. But then you should have bought the car for a steal, so you should have some cash to make it nice.
You'll probably want to do.
Leaky/torn intake tubes,
Fuel filter and pump
parking brake are probably rusted away.
replace all fluids, brake, oil, coolant, power steering, transmission and diff oil.
engine and transmission mounts
the PCV system is pretty flaky, so I recommend using a block heater and/or making sure the oil gets up over 100'C during the winter (ie. longer, harder drives, especially if you have short trips where the car doesn't warm up)
For all your mounts/bushings, I recommend going to Meyle HD mounts or M3 spec mounts as the stock pieces are filled with oil and don't last as long.
I'm just gonna stop there and reference this thread.