Engine shutters when accelerating and getting poor gas mileage

I suspect you have two issues. The shudder and fuel mileage sound like a misfire. The A/C only working on high speed is not related so we need to separate that issue out into a different post so that others that have that issue can find it. They will not find an A/C issue under this heading.

As for the shudder, does the engine idle smooth and only shudder when you are accelerating? Is the check engine light on? If so, we need to get the codes.

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

If there is no check engine light, is there a point at which this goes away? In other words can you reach a speed that it no longer does it or maybe an RPM that it goes away?

The light is interesting. Can you get a picture of this light? That I am sure will help figure this out if that is flashing every time this happens. Thanks

I see the picture but the light was not part of the picture. Can you describe the light? What does it look like when it comes on? Is it just a light or a symbol?