Please tell me if I should fix these problems and what they could cost me.

Front Driver CV Joint

Front right Turn light blinkes very fast

Heater and AC does not blow any air but lights on panel go on

Muffler Noise

Shifter automatically goes to the right to the overdrive without me pushing the button.

Please give me your thoughts. Its a 1999 A6

 

Right......

Fix the CV joint as its the most important. $400

Having one turn signal blinking very fast means one of the turn signal bulbs is burnt out, easy fix $5.

The A/C and heater concern could be explained if you have a solar panel sunroof, if not its most likely a blown A/C control head or relay.
Price undetermined.

Muffler noise, between $100-$500, depends on whats rattling.

WTF do you mean it goes into overdrive by itself!? Do you mean it flops over to tip tronic mode? Probably a bad shifter linkage assembly. $300-$400

Read the stickys and search the best you can.