First off, I feel for you. I've been in similar situations before I really started to DIY this car and I am still far from an expert. Not dissimilar to what you describe, taking it in for a simple service turned into a very long job (big red flag), and ultimately resulted in major transmission and cooling system damage.
I would focus on transmission first. My first check would be the transmission wiring harness and plug. Maybe they damaged it, or did not plug it back in properly/completely, or got some oil in there that is causing a short between the pins, which is causing the speed, etc. to not be displayed on your cluster.
Since they put on a new transmission pan seal, maybe they accidentally damaged one of the plugs/sensors on the valve body, but I would expect that to issue a transmission code to Durametric and throw you into limp mode (D - 4 blinking lights). You mentioned airbag and seatbelt codes, which again I can't imagine are related, but I would have the codes read again to see if they have reappeared, and at the same time make sure to have the transmission codes read. Just FYI, a transmission code will not cause your check engine light to come on, so unless one tells Durametric to check for them specifically they do not show up under the typical engine codes.
None of this explains A/C issue, but since your original quote mentioned to fill A/C, maybe they bled and did not fill? Can you tell if there is a change in rpm when you activate a/c? There should be a slight change when the clutch engages the compressor. I have never checked a/c system pressure on my 986, but have done it on BMW's and it is an easy check with a tool that your local auto parts store will usually loan out for free (or check for free).
Front radiators should activate when A/C is turned on. Make sure the snowflake light is on (sorry for being Mr. Obvious).
Coolant leak: wonder if they filled properly or if there is a bunch of air in the system (I see "top coolant" in their quote)? Make sure tank is filled to proper level and you can try to flip the bleed valve and drive with it open for a few days to see if it helps. Continue to check your coolant level in your tank and refill when the car has completely cooled off (if coolant level is low).
Battery: hard to say, but doesn't sound like there is a huge problem to me there, other than the shenanigans pulled by the shop, and the price for that battery is absurd. If I leave my car without driving for a week then the battery is usually drained. Maybe that's not normal, but normal for me.
Personally never had any issues with the instrument cluster and haven't heard this as a major issue with these cars. In the least it would be too coincidental that you have a cluster problem just after having work done by a shop that sounds questionable at best.
All the problems you are having sound very shady to me. We've all heard the nightmare stories of shops causing problems purposely: A simple clip of a wire or pull of a fuse that they know the exact location of is an easy fix that they can charge thousands of dollars for, but can be a nightmare for someone else to diagnose and find in a sea of wires, components, fuses, etc.
Ok, yes, I'm a bit of a conspiracy theorist, but I've been burned in the past.