The DDM (Driver Door Module) in these vehicles go bad quite often because water gets into the flat exposed switch crevices and runs down inside and eventually the electronics can be damaged. Swap with a local buddy if you can find one with the same DDM.
The design is that the DDM is a communications center, and sends data messages out to the rest of the vehicle. So if you ever lose control of things totally from the DDM, it may be a bad DDM or a broken data communications wire at the door hinge area where they flex more often than the other doors.
If only one or two functions are flaky, like the mirror control, it may be a problem local to your DDM. The door ajar problem could be in the DDM or in the switch in the latch area that detects door closure, and those can get corroded and need cleaning and lubrication. And the lock/unlock issue could be a simple dirty switch contact area on the PC board or the switch membrane.
Too many symptoms to be all from one cause, unless the DDM is just giving up the ghost. There are so many failures, that Ebay and the junkyards have a low supply, and the prices are going up. New at the GM dealers, they are sometimes on national backorder, and on top of that, you have to pay the dealer to program a virgin one to match your vehicle, a bery unfriendly design decision on GM's part.
I think your best tactic is to try to find a local trailblazer owner and swap with them and see if the behavior changes, then dig deeper into the door latch area depending on what happens with experiment #1.
Do you own a meter and have any electrical troubleshooting experience?