Units that are contacted during movement are not allowed to voluntarily move further, that is spelled out, and I think there is an example dedicated to that topic. Deployment comes at the end of the Movement Phase, Units that are contacted are not allowed to move, thus they cannot perform the action of deploying – which is described as getting out of that column they are in (4.3).

There isn’t actually any “charge” in ESR, but I’m guessing you mean, “move to contact with the enemy”. The answer there depends on which Units were contacted and therefore frozen, if they were not contacted, and therefore can deploy, a deploying Unit *is* explicitly allowed to move to contact with the enemy. So, potentially... yes. I believe this is noted explicitly on the Quick Reference Guide at the bottom of the Ploy & Deploy table.