Engine shut off while driving and would not start

Hello, do you have any idea where the smoke was coming from? Did the van overheat at any point? The smoke in the engine compartment is a concern. It may have something to do with why it shut down. Without more information, it's hard to tell what caused it. There are many possibilities. There is a recall on this engine for overheating concern due to a cracked cylinder head and it leaks engine oil onto the exhaust. This would definitely cause a lot of smoke under the hood. As well as a risk of fire.
Here is the recall information below about the cracked cylinder head and oil leak.
You may want to take it to your local parts store and have them scan the engine computer for Diagnostic Trouble Codes. There is probably something stored in the computer due to the shutdown. I would think the engine computer would record a code when something like that happens.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

https://www.2carpros.com/articles/engine-is-leaking-oil

Well, it may not be a transmission failure. The transmission, engine, vehicle body, and various other components all have computers or modules that control them. They all communicate on a network. Almost like your home internet network, except this is a bit different because all the modules are communicating (talking) to each other about all the that's happening while she's driving. So, if there was smoke, obviously something got hot to cause the smoke. Sometimes if for some reason the wiring harness was not secured correctly, it came in contact with the exhaust pipe or manifold. It would melt wires and cause all kinds of issues. So, if the transmission wiring harness got damaged somehow, and in this van the transmission is controlled by the engine computer (PCM), that could cause the transmission to go into Limp Mode, where the PCM will restrict the speed, the vehicle can go because of a fault.
I couldn't 100% say it's a transmission failure because of the No Crank situation. That leads me more towards a wiring harness issue. There's a good possibility that if the wiring harness became shorted out somehow (as an example, by touching the hot exhaust manifold) it would have also blown some fuses, and that would definitely limit the function of the vehicle.
So, if some shop automatically tells you, you need a new transmission. I would want a thorough explanation of what happened, where the smoke came from, and is there any wiring damage anywhere on the vehicle. Especially under where she could have hit something on the road and that damaged or caused these things to happen.
Don't let them just tell you, you won't understand why it happened, it just needs a transmission. And it being stuck either in 2nd gear or Limp Mode. There will most definitely be Diagnostic trouble codes stored in the PCM that they need to show you and write them down. We can tell you what they mean.
The reason there were no codes at AutoZone is because when she unhooked the battery overnight, that cleared the memory of the PCM.
Also, with lights staying on without the key being in the ignition points to a wiring or computer issue. Something is communicating with the Body Control module to keep those lights on.
I think there's more going on here. Don't let a shop take your money without a really good explanation of things. And ask us here if you're unsure.
Post a new question here if she's a shop and needs answers quickly. That way someone will be able to get to you faster.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

https://www.2carpros.com/articles/how-a-car-computer-works-pcm-ecm-bcm