Outline issues

Thanks for sharing the file.

Unfortunately, the entire compositions are somehow poisoned by numerous (often useless) clipping paths. The thing that looks like a rectangle on your screenshot is actually a (pretty superfluous) compound path.

A lot of clean up work would have to be done in case you are still looking for a reasonable (quick, possibly a single click) way to apply one single outline to the illustration. Of course, there may be some tricks to get a quick result, but at least this evening I don't have the time to offer some adequate approaches.

If the illustrations were properly done, the outline could be made with one single click (graphic style).

Yes, using a file sharing provider and posting a (public) link here is recommendable.

This way all participants may have a look at the file.

Can you share the Illustrator file (.ai)?

Trouble is the rectangle in it. So applying this via the appearance panel is not an option.

So basically, you make a copy of everything (via the layers panel. Put that duplicate on a new layer and lock the original layer. And then expand strokes and outline text and see that you can get rid of that rectangle whatever it is. A clipping mask?

Then unite all the shapes using the pathfinder panel and apply the stroke