miden Is it a shortened form of me den ("with not" i.e. without)?
No. Different vowels, to begin with.
δεν is originally from ουδέν, from ουδέ + εν "(and) not one".
μηδέν is similarly from μηδέ + εν "(and) not one".
μη and ου were both negative particles in Ancient Greek; I'm not sure exactly how they were used differently.