Cutting out, running rough, no power

This sounds like an issue with either the air intake or fuel. I would start with the mass air flow sensor and checking the voltage when you are idling and then giving it gas.

I attached the wiring diagram below to assist with this.

Here are a number of guides that help with understanding the MAF:

https://www.2carpros.com/articles/how-a-mass-air-flow-sensor-works-maf

https://www.2carpros.com/articles/mass-air-flow-service

https://www.2carpros.com/articles/how-to-replace-a-mass-air-flow-sensor-maf

Also, I am attaching the info from the manual on this sensor but in short, this sensor tells the PCM how much air is coming in so that it can match that amount of air with the proper amount of fuel. When they are not correct the engine will act like you are describing.

Also, we can check for codes and if there are some there that will help confirm this or point us in a different direction.

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

Let's start with this and go from there. Thanks