What kind of window is this? And how to open it?
Yep, looks like you hit it with Preston type, it's a screw drive that pulls the window in like a hopper window. Behind the cross-shaped part with the screw (threaded section) should be a part that spins on the threads and walks the upper assembly out, pulling the window along the screw. 

I'd get up there and remove the hardware and clean it up, since it's caked with paint and not gonna move easily, plus you'll find you need a long, looped cord/chain/bead chain to run the spinning part. Hard to describe, but start by pulling the assembly off, clean, and make sure the window is not painted shut (sealed with paint). 

Personally, I'd make sure the window opens easily with the mechanism off before moving forward. That style opening is designed to keep the window in place if there is wind, and be easy to open from floor level. Other types of closures used on high windows were a lever with a loop in it that you would use a pole with a hook on to open the latch and pull the window in. 

Here's another style shown: Transom Hardware, oldhouseonline.com