Hi and welcome
No idea of part number, I may have it at home on an invoice though.
Only use the MB oil, it is just not worth risking a non compatible oil. The gearbox on the 320 and 270 will be the same so the oil capacity and filters will be the same.
There is a post on here by Black55 (Ollie at PCS) on how to do the change. Try searching.
Whilst a perfectly possible DIY procedure you really do need a proper lift to get the car high enough to remove the sump pan so it can drain more fluid and then be thoroughly cleaned. It is also vital that you get no dirt, lint etc anywhere near the sump or gearbox internals. It is also difficult to remove all of the old oil without special knowledge and tools.
It can also be a problem to remove the sump bolts as they can sieze and sometimes need drilling out. If they come out then you must clean the threads before putting them back.Not sure if you need thread sealant.
You also will not have a transmission dipstick unless you buy one so getting the level correct can be difficult as the dealers and indies use the STAR computer to monitor gearbox temperature whilst filling, checking and re-setting. I would very strongly suggest you get a good indiue to do it (No idea where you are but Ollie at PCS near Horndean is very highly thought of) I was quoted approximately £185 for all parts and labour.