The best way I’ve found to deal with this aspect of daily life is to provide much greater stress on a regular basis. That is, do heavy weightlifting exercises, and other high intensity training (such as sprinting). Your body will adapt to be able to deal with things that are extremely physically demanding, and everything else becomes easier.
Shoulders are involved in all upper-body exercises, so they’re easy to make stronger.
The neck is challenging. The problem is, you can rotate it in three dimensions, and I haven’t found exercising with a neck harness to be effective even in one, due to how unwieldy it is. I’ve resorted to isometric exercise alone for my neck, but that actually really helps. Frequently, while driving or at the computer, my neck will get sore. At these times, I just press really hard against my head, and resist that motion using my neck, in all six ways that the head can rotate.
Wrists/hands are easy to make healthier. I use Captains of Crush grippers and Expand-Your-Hands bands, and do wrist curls and reverse wrist curls.
For eye and face muscles, I have no idea what you mean. I can say that my eyes twitch too much when I have too much coffee, so I switched almost completely to decaf, and that’s helped out a lot. What problems are you having exactly?
Also, a healthy diet is important. You need protein to build the muscles up, and you need to lose fat, if you are partially having problems due to the fact that your head and arms weigh too much. Good posture is also important, when you’re sitting in a chair that long, and it’s a lot harder to have it when you have excess rolls in the way. I’ve been skinny, fat, and in decent shape, so I speak from firsthand experience on this.