Nice purchase. It looks very clean, you can get new center caps from the dealer as it can not be shipped for some reason on Ford Parts. Part #
Official Ford Parts Site | Buy Motorcraft & OEM Ford Parts Online | FordParts.com
I will try to help as much as I can on your questions.
1. Thermostat be ready for some what of a mess, place plastic covering over front of motor as to not get any liquid on accessory drive components. Also keep in mind if the intake manifold is plastic depending on how many miles are on the car, the manifold tends to crack. There is a replacement from Dorman which is all aluminum. Here is the schematic for you on Ford Parts.com show intake and T-stat :
Official Ford Parts Site | Buy Motorcraft & OEM Ford Parts Online | FordParts.com
2. CD player should be plug and play, aftermarket units are readily available through Best Buy, or ebay or amazon depends on what you want. *Might want to invest in a pair of Lincoln Town Car repair manuals that where used to service the car at the Lincoln dealer. This will show you how to take off the trim components so you do not bust any clips or retainers. These are available on ebay. This was the cheapest I could find
might want to snap this up quickly:
2007 LINCOLN TOWN CAR Service Repair Shop Manual Set W Wiring Diagram Book OEM | eBay
3. Air bag light is a code go take it to Autozone to get checked. Then cross reference with some codes here:
Complete List of OBD Codes: Generic OBD2 (OBDII) & Manufacturer | Car OBD Diagnostics, ECU Chip Tuning & Auto Repair Support
4. It might be just a fuse that burned out. Check your fuses in the owners manual to see where its located. Either under the hood or under the dash.
5. Battery might have a bad connection some where. Look at the ends, are they corroded beyond means? Might be time for new cables, also check to see if its a code as well. It very well could be.
6. Air suspension leak maybe a simple fix like a new o-ring, RockAuto sells an O-ring kit:
2007 LINCOLN TOWN CAR 4.6L V8 Air Suspension O-Ring Kit | RockAuto It also could need a compressor. I would try looking at too see if its the o-ring/s..
7. The keypad code should be on the trunk hinge when you open the trunk. It will be a long sticker.
Hope this helps you out. At least it gives you some kind of idea to trouble shoot. Autozone and you dealer will be of the best of help as well as all these great people on this site.
-Ray