It does not matter to have the links since those products are well-known in the photography community. You are asking for multiple advice in one question but if you take all the requirements as a whole, then it is possible to get a set of suggestions that would work best for you.
The answer to the first question is obvious: Chose the Nikon D7500 over the D5600:
- The D7500 is a much faster camera: Its top 8 FPS speed is 50% faster than the D5600. This gives you significantly better change to get the peak of action and more photos in focus when shooting martial arts.
- The sensor in the D7500 has a higher maximum ISO which allows you to use faster shutter-speeds to freeze action.
- Autofocus of the D7500 is much faster and more sensitive with 51-Points of which 15 are cross-type, compared to 39-Points with 9 cross-type.
- There are more controls on the D7500, including dual-control dials, which lets you operate the camera faster which greatly helps for action photography.
- You can view the full comparison of these specifications on my site, here is the direct link.
For night sky photography, bright wide lenses are generally preferred. Although changing the focal-length is a create choice, it is more important that the lens be bright. So out of the three options, I would recommend the Rokinon 14mm F/2.8 with the Tokina being a good choice too. If you can find a F/2 version of something wide, you can use that too. There is no need to worry about AF because most cameras cannot focus reliable when the environment is too dark.
For martial arts, a 70-200mm F/2.8 is usually a good option as long as you are not too close to the action. The AF should be fast as it is difficult to follow such quick action manually. Stabilization though is not important since it compensate for the photographer's movements and not the subjects. You would be shooting at 1/1000s and faster, so you must be above the hand-holding limit. You only gave one choice for this and I do suspect that this lens does not focus very quickly, so I recommend you look at AF-S versions or equivalent from third-party. Sigma makes the S 70-200mm F/2.8 DG OS HSM which should be a good candidate.