Nice looking 2013 you have! We bought an LTZ a few months ago. The passenger side window does end the down cycle with a thump! The others less so. Our windshield washer fluid line came loose in the back so I just put it back together and it's been good since. The inside driver door handle is broken on ours as well, that is the most annoying thing to me so far. At first I never noticed the air compressor coming on but now I do. It's pretty muffled but sounds like one of those little cigarette lighter spare pumps. The hill downshifting startled me at first but I read the manual to discover it was a good thing. It's a really good feature when towing in trailer mode!
My only regret is not buying one years ago! Well I do have a slight regret of not buying a newer Tahoe but for the price the 2013 will have to do. I could do with a little more power and better cooling when towing but I have towed with several vehicles through the years and it's as good as any of them so I shouldn't complain.
Get an owners manual and enjoy!