There are at least 11 darkrooms in Berlin listing on Ilford's darkroom finder site - a mixture of rental darkrooms, tuition darkrooms and private darkrooms that are willing to offer access to others.
To answer your question as best that I can:
Pretty much your only choice for a wide range of analogue materials is Foto Impex:
http://www.fotoimpex.de
They own the Adox brand and produce a wide range of chemicals, paper, film, etc plus produce Adonol (based on original Rodinal formula) and stock items you might not be familiar with such as the chemicals from Moersch and Spur and, naturally, they also stock all the usual films.
You can also pre-order stuff through their website and have it sent to their shop in Berlin (good idea if you are after something not run of the mill as they do not stock everything in the shop).
They also have a processing service. I have never used them but, judging from the quality of the prints on display, I wouldnt assume they are that great.
Pixel Grain are a pretty big lab in Berlin - but again I have never used them.
http://pixelgrain.com
Viertel for achy is another lab in Prenzlauer Berg that always seems busy - but again I have never used them.
http://www.vv8.de
Other specialist labs that I have heard of are:
http://www.schwarz-weiss-labor.de
http://www.ulrich-hagel-labor.de
Depending on the actual dates you will be in Berlin, I might be able to help you out with processing yourself in my darkroom. It is no palace and located in an old arts complex but it would suffice for processing your films. Water is terrible (victorian pipes) but as long as you use distilled water (costs 2 for 5 litres) for mixing developer and final wash there are no problems.
The only rental darkrooms that I have heard of (but not used) is Ida Nowhere:
http://www.ida-nowhere.com
By the way, when you are in Berlin you must check out 25 books. It is a goldmine full of books made by photographers, small independent publishers, etc.
Bests,
David
www.dsallen.de