Why is my engine missing out and engine light on?

It's pointless guessing the answer. Get all of them sorted out or the fault codes will return and the problem won't be solved. Go to two or three independent mechanics and get there opinion.

Don’t neglect the basics like a tune up including plugs and a fuel filter, etc. if a check engine light is present get it checked for free at att parts store, mine was thecssnecwaybsvd had a loose fuel injector plug in themso wiring harness and a plug wire was bad. Keep it simple, you’ve got this!

releasing the gas pedal and it gets going again
not very safe

is the engine light on
could be any faulty sensor in this engine diagram

maf clean might help
if a spark issue needs chasing
it could be a fuel problem
maybe bad fuel or blocked fuel filter

[PDF]GM Motor Company Group Diagnostic Trouble Codes

https://edgeproducts.com/app/.../customer_support_article-pdf-40.pdf
GM Motor Company Group. Diagnostic Trouble Codes. Here is the list of DTC's. This is a HUGE file (48 pages ) so it's probably easiest to use your scroll function ..

Not without having a transmission shop look at it.
Could be a failed pump, valve body, even something inside the differential. But if it involved the axles you would also not have any hold in park.

Don't think it's missing. Low fuel. Check fuel pressure after regulator.

Please elaborate on "runs rough"
Is it slipping gears.... hesitating on acceleration... missing... smoking... backfiring?

Thanks!!

It sounds like one or both of the drive axle inner joints are worn out. This condition will give a very pronounced vibration on acceleration only and will be worse with increased speed.

Check wheel balance,
check steering linkages for loosness - such as tie rod ends, steering rack linkages etc,
check driveline for worn/loose joints and bearings.

If the engine light is on, a code scanner needs to be connected to it to find out why the light is on. It could be one of the sensors causing it. Take to autozone or advanced auto if there is one near you, if not call a repair shop that can do it. Autozone and advanced don't charge. Takes about 30 seconds.