Your existing AC/Heater control panel uses vacuum tubing to actuate the blend doors, air conditioner, heater, defroster, etc. The closest thing to electronic in that system is the lightbulb behind the switch. There is no provision in the BCM for any other kind of interface. The auto mirror, btw, has nothing at all to do with temperature control. If you look on your dash near the windshield in front of the driver, there should be a small red lensed sensor. That is the ambient light sensor that is used to control the headlights, dash lights, etc. If you look to the right of that, you will see a place for another sensor. That is the one that senses light amplitude and provides input into the BCM for use in the ATC. If you look on the front of the dash, between the glove box and AC control, you will see a little vent looking thing. That is where the inside aire/humidity sensor goes that provides an input to the BCM for the ATC (you don't have one, just a place for it). The automatic climate control unit found in the Grand Cherokee Limited (not in Laredos, not no way, not no how) uses electronics to control the blend doors. It is connected to a system communications buss that transmits data from and to all the onboard sensors, including vehicle speed, and the ambient temperature sensor located behind the grill. This communications buss (which utilizes twisted pair wiring) allows the BCM, PCM, driver door module, and passenger door module to communicate with each other to proved the inputs the ATC requires in order to function.
In other words, no, you can't just swap them out. It would be far more practical to simply buy a Limited.
There is no Hepa filter in the A/C system for your Jeep, so you are going to smell any noxious oder you happen to drive through (turn on recirc to avoid this). If you aren't driving through somebody else's exhaust fumes, and still smell exhaust, I will guess you have the inline six 4.0L engine, and it most likely has a cracked exhaust manifold (very commone with those engines). Get it fixed before you kill yourself. Aftermarked headers are plentiful and cost less than OEM exhaust manifolds. If you decide to upgrade the entire exhaust system, limit your pipe size to no more than 2.5 inches.
What is the existing sound system? If it says Infinity Gold on the speaker grills, then you will have an amp underneath the driver's side passenger seat. This will complicate your stereo upgrade, depending on how you go about it. For ease of installation, customer support, and complete packaging of everything you need, I recommend Crutchfield's. They even have a couple DIN 1.5 head units you might like. For a less expensive place to shop, Walmart sells stereos. Circuit City is somewhere between the two, I hear.
Sunvisor clips are readily available from the dealer for cheap, as Hunter said. Otherwise, eBay always has some listed.
Go to Auto Zone, Advance Auto, or the like and purchase a recharge kit for the R-134a A/C. It is very easy to do. I suggest buying a can with dye in it, then looking for leaks.
A bad door lock actuator may be your problem, but before going to the trouble and expense of replacing it, check the wires in the door jamb. You'll have to peel back the rubber boot to see them. It is very common for wires to flex until they part in there. If any other doors lose functions such as locks or windows, check the driver door wiring first.