Can I use a 2004 Chevy trailblazer front differential to replace my 2005 awd Buick Rainier front differential

My mechanic says it is because I have to buy all new tires and be put on at the same time??????? Help P. S. It shakes too???

battery dead, wend I jump it , wont start, code p2101

It looks like interior lights maybe flickering a little.

Is this expensive to repair? When I am driving in a straight line, it is ok. It hasn't effected mileage. Every time I try to make a sharp turn, it seems the wheels jerk. Is this going to be an expensive repair? Another issue is the rear air shocks loose air. When car is running, it seems like rear end goes up again. I never hear the load levelers working anymore. Thanks for your help. I'm a 74 year old female widow and need some advice. Thank you for your help.

Head lights, park light, dome lights will not shut off after engine in cut off.
Then sometimes the light will not come on. What could be wrong and an
approx. estimate.

Lights are staying on. Last night had to unplug battery cable Then at time they won't come on. This is intermittingly.

Air will come out the defroster and feet but not out the vents. No issues with fan speeds or volume of air.