It would not be too hard to track all key presses and mouse interactions to a log, send that and then replay. Wouldn’t even need a video file for that and the result file would take up a lot less space.
It is possible, but it may be not entirely trivial
I would recommend starting with:
You mentioned 10 FPS would be enough for you, so that might make things a bit easier; you’d simply only capture 10 frames per second, which should make saving the images less hard on the machine.
Any “extras”, like mouse-cursor or keypresses would have to be visualized in the game. Like, you could create an “in-game cursor” that follows the mouse position (should be easy to set up with UnityGUI, there might even be ready examples in the forums or on the Wiki).
Finally, you’d have to visualize the keypresses somehow, which should also be quite easy to set up with UnityGUI, but it obviously does require a bit of programming.
I’ve done something like that. I recorded user input like keyboard, mouse movement and stuff, recorded that to memory and later played that back in a slower, non-realtime speed and capture screenshots to assemble a movie. For the movie assembling I used an external tool, but with the right knowledge you could do it in Unity or, more easily, send the trainer the recorded input events. Way easier and file sizes are way smaller.