A language learners’ forum

Couldn't find any exact information and couldn't contact the moderators to ask about the Private Message function. How many posts am I supposed to make to get this feature?

It's in the FAQ.

@ new members, please try not to make too many pending posts. Get to three and then post normally

OK, Thanks. By the way, I am a new member only technically, as I have contributed quite a few posts back in the glorious days of HTLAL

Yeah I think I remember seeing your username Welcome!
In this context new means "users whose posts require approval by the mods".

I can't seem to find a way to delete PMs, and I only have one space left in my inbox.

You can tick the boxes on the right and then at the bottom there are options for marking them as important or deleting. I see these even if I make the window really narrow so it should work fine on a mobile device as well. (I'm using firefox)
If this doesn't help let us know which browser etc you use