I don't know about the exact rules but you would be fine with the 6 month time, sounds reasonable to me, no need to change car registration as long you are registered at your home in Turkey, all depending on what sort of visa you are holding, make sure you got one explicitly for Germany and neighbouring countries!
there was a case where a few Turkish girly students had a visa for studding in Poland only and wanted to visit some friends in Hamburg/Germany over a long weekend... well they got stopped by the German border police and arrester, accused of being silent seeker regarding there Polish visa that didn't allow for all EU-countries... so make sure you are allowed to move around all of the EU or at least for the countries you want to see.
Paper wise I would strongly recommend a appropriate insurance that cover's all the EU-nations, being on the absolute safe side you may even consider to get a international driving licence of your local department.
The part of your plan to buy a bike in the EU, ride it around may get a bit tricky... on a tourist Visa, but... if you are legally working in Germany you would have in definitely a (working permission including the right to stay for a limited time which can be renewed) in that case you have to be registered with a residential address, which in turn let you register a vehicle.
good news first:
you can buy any bike.
you can get a export registration in your name including insurance on tourist visa.
you can ride the bike with your international and Turkey licence.
the export registration only allows you 3 month to move around in Germany.
get the bike registered on to the name of a "trusted" friend with legal residential address in Germany, can be a Turkish landsman with a so called "Aufenthaltsgenemigung" (permission of limited stay) or you may register it in your own name if you got a "Arbeitsgenemigung" (working permit that will containing a permission to stay), registered and insure the bike on German plates and you can ride around as long you like.
have a good look what your Turkish-foreign-department is recommending on there web page, I'm sure they will cover "all" your questions. A step further... yes believe it or not... regarding the large amount of Turks living in Germany you will find a lot of German governments information written and published in Turkish language as well. yes you can even make your written theoretic German driving licence on Turkish printed forms.
hope this could help a bit, have fun.. and a good time.
Last edited by spooky; 23 Mar 2010 at 08:34.