Should I caulk the top and bottom of my windows on the outside?
In these photos, it looks as through there is a foam backing strip -- this was probably put in to form a seal a long time ago, when the gap was smaller. If this is the case, you might want to get another foam strip and put it in the gap to seal it.

Also in the second picture, it looks like there is an old caulk joint at the bottom of the image, which has cracked over time.

It's possible that these gaps get larger and smaller over the course of seasons, but I don't think that caulking them on the edges would build up enough force to mess anything up. My guess for why they're there at all is that the components were aligned flush when the house was constructed, and there was no need to caulk them.

The major downside I'd expect is that removing those window frames might be slightly more of a pain if you ever decide to have them replaced.

The answers on a previous question regarding this subject mentioned a couple things about trapping water in, so this might be a good point to start off for more research:

Should Caulk be used around vinyl windows