how do I get a caption sticking with the image?
Use the element figure, containing graphical content or the img element for raster images and the element figcaption containing text for the caption.
I don't understand what you mean.
I tried grouping my image and caption together. I tried grouping them in caption setup under object. Nothing works
Try taking a look at this:
As O.H. suggested, I think that's what you need.