I have 06 H3, w/ adventure pkg, 5speed. 11K miles. My First GM product.
-I have seen many a comment about GMs batteries. So I am not surprised some are bad. Not a deal breaker for me.
-Onstar Module - Mine (what ever it was) was not working when I bought the truck. Onstar couldn't get a data connection to the vehicle. Replaced under warranty. Not a deal breaker to me.
- Serpentine belt. That seems odd. But who knows. It was replaced under warranty. Not a deal breaker to me.
- Door Rattle - No idea. That should be fixed by dealer.
- Total Brake Failure - Again no idea. Should be fixed under warrenty. Makes me a little nervous.
- Wind noise roof marker lights - If you search here a bit you'll find this has been a reported issue since the first one rolled off the assembly line. Unfortunately you were not aware of it when you bought it. I understand GM has been trying to get a fix for this. I thought I had heard they have one, so that should be fixed (warranty). Not a deal breaker for me.
- TPM sensor problem - not sure what your issue is. Many here, including myself have reported and noted that the TPM will warn you on a cold winter day, and then go off when the tires warm up. I don't mind it (as long as it goes off after a few miles). Not a deal breaker for me.
- Driver door Harness came apart - No idea. Should be fixed.
- Transfer case overhaul - similar to Marker light noise. There has been some reported issues with 06 transfer cases. I believe the company making them for GM screwed up a bit. Left some lapping compound inside and after ? 5K-15K miles, it chews up your gears and you get a new transfer case. Yup. It's a bummer. But I am not putting too much fault on GM for that (until it happens to mine

). I think it is a pretty small (not wide spread) issue.
So it looks like a few things out of the ordinary have been going wrong. Well. Sometimes there are lemons, hence the need for the law. From whet I hear, tese issue don't qualify as lemon law issues unless they are reported, and cannot be fixed, or don't get fixed. Something like that.
I feel your pain. I love the truck. I am willing to put up with a few things because I love it. Hummer has a better reliability rate than Land Rover and Saab (just saw a JD Powers report on it today for 2006 cars), so that's good.
Good luck. I hope everything gets fixed and you have fun with it in the end.