At first thank you for your answers!
Sadly I don't have access to an ultrasonic cleaner, but at the university we have a nice hot air soldering station and good flux available.
I will try that tomorrow on the parts that are not solderable by hand (at least for me).
Until now I cleaned the rest of the meter and cleaned/repaired the traces around the dual mosfet. I desoldered it, cleaned the PCB with alcohol and used a glass fiber brush on the difficult spots. Later I used a self-made mixture of rosin and alcohol and coated the traces with tin. On the chip I also had to scrape off the rotten tin before it was solderable again. Soldered the mosfet back on and tadaa: multimeter turned on after hooking it up to the lab power supply! I was able to go through the menu, but I am not able to measure a thing. Only a decimal point is displayed regardless of which range/mode is selected.
Regarding to the 3 "CT2 16Z" I found out that they
are presumably multi-LDO packages from Ricoh. Likely a RX5320X series chip. If anyone is able to find the marking specifications for this chip please feel free to share the exact model and voltage! The only promising link I could find with Google is unresponsive (www.aeneas.com.cn/PDF/Ricoh/new/MARKING.pdf).After further investigation these chips are more likely level shiftersTwo things to add:
1st: I made a mistake with the product series, it's actually called the "Star-Series"
2nd: The beloved MetraHit Energy has the same design in accordance to the battery holders. So better get your batteries out there when not using it!