here is an example of applying rotation to the object and then moving along one of the rotated axes, you can press buttons (more than once, if you like) and see how rotation/translation works in this case:

that’s entirely up to you, you want to move along a vector, the vector gives you a direction, it doesn’t tell you by how much you move along it.

If your rotational vector is something like velocity, you can calculate its length and move by that amount.