Alternator burned now problems ensue?

You have 11 codes set now?

Well, with the stalling now, I think I know what's going on, I looked up 4 of these codes, P0627 Fuel Pump A Control Circuit open
P0645 AC Clutch Relay Control Circuit open
P0685 PCM Power Relay Control Circuit open - This I assume is the ASD Relay
P0688 PCM Power Relay Sense Circuit open

But all these components- Control circuits are in the PCM C3 connector.
But also, PCM C3 goes to C1 of the TIPM (2nd diagram). I'm not sure if you had unplugged any of the TIPM connectors, but this might be a connector issue since these problems were not there as far as we know before the repair
I would stick with the Torque scan tool for now, I think Torque also has live data. Are you using the ELM 327 with the data link connector?
Looks like Electronic Throttle control.

The TIPM is more like a smart junction fuse panel, it has canbus data network circuits and works with the PCM. I dent like a 30volt spike, it's possible that is due to the solenoid transient shut off voltage. But I think the stall out issue has more to do with these codes, try clearing them all, and check that C3 is connected fully. These TIPM connectors look to be on the underside of the module, if you can see in the diagrams 1, 2 below. I'm not sure how much those connectors got moved around during testing. After you clear the codes and check the connectors, let's see which codes come back first. It's clear the ASD Relay is powering down, that's powering down the PCM, and it's a domino effect of power loss. Hopefully this is just a connector pin issue. Diagnosing a failed TIPM is going to be very difficult.
There is a recall on the Fuel pump relay inside the TIPM failing causing a stall condition, but that doesn't make much sense since the vehicle ran before the solenoid replacement

If you can pull up any live data on the Torque for the PCM, it would help to see what is cutting out first. The TIPM has integrated circuit boards and power bus bar. And it can also set trouble codes itself. They won't be P codes; it will be more of U or B type codes.

Battery voltage looks too low in these scans, did it stall out or are these scans just key on engine off? These PCM power relay codes 685, 688 are the concerning point, for some reason the ECM or TIPM is shutting down the ASD relay and then the PCM is detecting that power failure (p0688 power relay sense circuit). You might try shutting everything down, unplug your scan tools and unhook the battery negative for a few minutes and see what happens. If your battery has a battery current sensor on the negative post make sure not to over tighten the clamp. Some of the TIPMs fuses might be encased and need a close look at to verify they aren't burnt. Can you reach the cam timing solenoid you replaced? Or is that under the intake? This has to be some kind of connection issue.
This vehicle has a wireless ignition node (module), maybe that scan tool is interfering with some communications on the data link connector.

There looks like there is another power distribution center with some higher amperage fuses, usually those are in small plastic cases. I would check all the fuses in the vehicle you can find. Ive been looking through service info for any procedures after a battery disconnect, but havent found any. With codes setting like they are, the only logical explanation is that some connection has been disturbed. If it was something to do with the anti theft or alarm system it wouldnt be setting those codes. And that you had a successful start up for 15min. Ill ask some other technicians what they think might be going on. It seemed like a simple enough repair. The only thing that comes to mind is harness connections.
Did you have any issues with stalling before the solenoid replacement? Or no start, or just this code setting (p0013)?
And out of the 11 codes, were there any for security system issues?
Ive posted the vehicle on a forum for All Data, lets see what some others have to say on the situation.

So, you're not getting any of the other codes you had on earlier scans? And yes, I was going to mention the cam sensor, but that was kind of useless at the point where it wouldn't run. Another possibility is that those wires shorted out and took out the ECM driver for the cam timing solenoid. I have seen Jeep ECMs take out drivers many times because of circuit design like this, If you do try a cam sensor, you'll have to do a cam/crank relearn procedure. But since this is a circuit code, you can try a new cam sensor and see if that specific code comes back (p0013). Since you don't have a scan tool with special functions right now, there is no way to do a crank relearn. But since the beginning of this, especially with the alternator issue, I was worried about that ECM driver, but you did have voltage there in the after the repair. Does the vehicle run now without stalling?

I was hoping that the live data would have more specific data PIDs like cam timing "Actual" and "Desired" and that would tell us if the timing was able to change or not.
I'm going to look up more info on the cam sensor, because I don't think the vehicle would start at all if the cam sensor was not working, but I don't know how many this has either, so ill check that right now.

It depends on the condition of the alternator, but what initially happened with the old alternator could have potentially damaged the TIPM, they are known for failure. The code that is setting is camshaft position actuator circuit open code, but we are limited here on options. You don't have a scope or any to monitor position sensors, this vehicle only has 1 cam position sensor. It's a 0 to 5volt three wire sensor, so it's a hall effect sensor that will make 0-5volt square wave signals to the ECM in time with the crank position sensor. Since its still stalling out you can try blocking off the Purge valve and see if that will stop the stalling, You do have the historic Evap code, If there is a vacuum leak through the evap system, and the Purge valve is still being turned on, that might account for the stalling and it worth a try, I'm pulling its location right now, give me a sec.
In the 2nd diagram in Green is the strut tower on the driver side, and the Purge Valve is what the ECM uses to pull vapors into the intake manifold. You can try unplugging it first (electrical connector), and if it still stalls you can take a line off coming to the purge valve and block it off, this is just a shot in the dark. But technically the engine could start purging the tank a few minutes after start up.
Next, we would just have to try a cam sensor.

Refresh this page again and it will show my last posts.
That Battery voltage is still reading low, I'm not sure if that data is after the stall out or not, but it doesn't seem to be charging correctly either. I don't think 11.8v will shut down the vehicle, but that alternator may have done more damage than we know. If the AC voltage ripple got high enough it could definitely damage the PCM or TIPM. There might be multiple problems here.

Yeah, the ECM is able to monitor the voltage on that solenoid control circuit, its seeing an issue right when you turn the key on. So, there is still an issue on that cam timing circuit, but that really shouldn't cause it to stall out. It might need a number of key cycles before it can set any of the other codes, since it's probably not running long enough or another possibility is the charging system voltage, check that while its running, leave the multimeter right on the battery when you start it up, That way you can see how low the battery drops during start up and catch the charging system voltage before it stalls out. It's really difficult to tell what is happening, not being at the vehicle with you. Do any warning lights come on the dash just before the stall out?

Okay, no worries, hope everything is okay. Glad you mentioned the Electronic Throttle control warning light, I wonder if the vehicle lost its learned idle speed memory with the battery being disconnected. chat with you tomorrow,
I do think it might need an Idle Relearn procedure done with that light coming on. Granted there is still something going on with the cam timing solenoid circuit. But we need to get this thing to idle at least for you. The only way to read any of the TIPM data is with a capable scan tool that can read into more than just the engine computer. There are so many modules on modern vehicles you wouldn't believe it. I had a couple of guys suggest checking the charging system while running, make sure it's up to 13-14volt range. If it's an idle relearn issue, since the throttle plate movement is how the idle is controlled now, no more idle air valves anymore, if you can put your foot on the gas and see if you can keep the throttle plates open enough to keep an idle, we would have an idea of what's going on. So, check that, the charging system voltage, possibly unplug the Purge valve, see what you come up with. If there's a low charging system voltage, the ECM might try to raise the idle for that reason, or cold engine as well.

This a manual Throttle Relearn procedure for a Chrysler, I don't know if this will work in your situation, but anything is worth a try right now.
This is the video from that, he waits until the check engine light starts to blink, and then tries the relearn with the gas pedal, so watch the video first, I will post any further info I come across.

https://www.youtube.com/watch?v=uf5Cg5SyrJ8