Problems With My '02 A4

I have a few questions, but first some background info:

I drive a 2002 Audi A4 1.8T (quattro) Manual Transmission
I bought the car off of ebay motors in October of 2004 with 58,600 miles on it, now I have 62,900 on it and am having a few little problems with it.

First of all, when I bought the car, I didn't check to see if the windshield wipers worked, and unfortunately they do not. Upon trying to clean the windshield with the wipers and windshield washer fluid the wipers would only extend up like an inch or so, pause, and then kinda return after a second or two (as if they had completed they had completely extended all the way up). I figure that either the motor is shot, or there is something blocking the wiper from its full extension.

Secondly, When I am driving at speeds of approx. 20 MPH or more and I turn the steering wheel to the right (even ever so slightly) my car makes a loud humming noise and it vibrates a little bit. This happens whether I am in gear or not. This doesn't happen when I turn to the left. I have consulted one person (not an authority, just a friend's father that owns a little car dealership) and he says that its just a bad tire, that the previous owner probably didn't rotate the tires often enough. But then again that is just his speculation.

Thirdly, I am having a little bit of trouble when I am starting up my car. Like for instance today I tried to start it, and it wouldnt turn over. It took like 15 mins of trying to start it before it finally turned over. It has been gradually getting a lil worse. But today I was like WTF?

Fourthly, When I am in 2nd & 3rd gear, sometimes I get a little bit of a stutter (very slight, but noticeable) and the acceleration seems to almost "plateau".

And fithly, In my manual, it says that I need to service my car every 10k miles, since I have gotten my car the service light has come on when I start my car up, and when I press the "wrench" in the instrument panel, it says service. Just wondering if it is really worth the $$$$ to go to the dealer.

Thanks