Adding background to image series - And how to save as Gif?

Hi there! I've learned how to place a series of images in a timeline, and have the timeline animate in a way that looks like an animation. But I have two big problems.

First, I would like to add one static background to all the images, they are currently sitting as layers, and have them exported as PNGs with the background on each frame, each image. I can make the background stay in Photoshop, but the export does not include the background image.

Second, when I save as a converted GIF file and open to look, it doesn't animate. It just sits on the first frame as a still image. How do I make this work?

Thank you very much.