I don’t know about 
overdrafts, last time I tried to get one (just to try it out - I don’t like easy access to debt) they said it wasn’t live yet. There is some info here if you’ve got the time to read through it all (I would’ve done it but it’s way too late tonight and I’m so tired) but the general opinion is that it’s bloody expensive (which I guess is fair enough - Monzo has to make money some way and I’d rather see them make good $$$ that way than pretend to be cheap but then scam you with fees every time they have the chance).
You should definitely apply for the current account preview, it seems they’ve been giving them out like peanuts lately, even Danny eventually got one. 