How to repair or at least hide cracks in wooden door panel?

You are correct. To get that panel out, you'll have to pull the top rail off the door, then the panel will slip out. You can then glue it up and glue the rail back in place. However, it's not that easy, as that top rail will be well and thoroughly glued in place.

• You may want to try staining the edges of the cracks a dark color so that the bare wood showing through doesn't stand out.

• You could put some wood filler in the cracks, if there are pieces missing, then stain that.

• If the cracks have made the panel loose enough that it rattles, you'd probably be able to carefully pull the panel apart at the cracks, and force some wood filler in. Then squeeze the panel back together. You do not want to leave the gaps wide enough that the panel cannot move or you'll end up with more cracks due to seasonal expansion. The filler won't hold quite as well as glue, but, since you won't be able to properly clamp the panel, you'll have some glue or filler showing, and you'll be able to stain the filler to match, but wouldn't be able to stain the glue.

If you do want to attempt to remove the top rail, I'd suggest asking a question about how to do that Woodworking. There are loads of experienced wood workers there and you're likely to get an answer about how to properly loosen/soften the glue to get it apart. That would be the better solution, but it won't be easy.