How to unscrew this uncommon type of screw?
Depending on your stair, lighting might be the responsibility of the council. If there's a sticker/notice that has a number for "concerns/ complaints", they'd be the right ones to call. If there's nothing posted, it might be a communal thing. Part of the reason I bring this up is that the replacement bulbs for that lamp seemed really expensive when bought in small quantities. (Or maybe that was just me being a cheapskate. From memory, it was just shy of a tenner.)

But a pair of small-ish needlenose pliers should allow you to unscrew them. If you're naughty, replace with a normal bolt. 

If your ceiling is high, be careful on that ladder.