दुखी / ऊदास ... do they mean the same kind of sad, and one is from Persian, the other from Sanskrit? Or, do they actually have slight semantic differences?
Is the usage of हो here a general principle of the form, or does is mean that "tum" is used for adressing the person?
Because you don't usually explicitly say तू/तुम/आप when ordering someone, there are only really two cases here:
Ordering someone in general: दूखी मत हो!
Ordering someone you respect (which doesn't really happen very often): दूखी मत होइये!