Is there a script to batch auto change images to 350 dpi, specific width, and then save as jpg?

Two things you need to know:

One, the jpeg file format is extremely limited. It does not allow 16 bit depth, layers, transparency or alpha channels. If your file has any of these properties, jpeg is off limits. Then you need to save as a copy with these properties stripped or "dumbed down". That's why you're getting the popups. Also, the jpeg algorithm degrades the file with every save. Don't resave jpegs.

Two, an action to save with a specific ppi value is never a good idea. If you're using the ppi number to resample, you're destroying your files. That could be a deliberate decision on a case by case basis, but not as an automatic procedure.

If you're setting a new ppi value without resampling, it' a total waste. It doesn't change the file at all, just a tiny bit of metadata.

A much better idea is to keep your master file archive as TIFFs or PSDs with all data intact. Then you make actions to save out copies with specific properties. These copies you don't need to keep, because you can instantly recreate them from the master files.