Disclaimer: I have not ridden any of the boards you're looking at!
That said, gonna try and help you out and show the differences between the boards for you.
From a quick look, the Nitro and K2 are both flat boards(K2 is flat with rockered tips). Last year I bought a board with a flat profile and it's a fun profile to mess around on. Not as catchy as a camber board and very predictable handling. Didn't get to do any powder riding so can't say how the profile performs there.
The Rome boards are both hybrid camber. The Crail has camber between the feet and rocker past the bindings. The Headline has camber extending farther past the bindings with rocker towards the tips.
I like hybrid boards as having the mix of both profiles gives you advantages of both, but they do behave differently than pure camber/rocker/flat boards. Nothing big, but they have their quirks that you may need to get used to.
As for sidecuts I believe both the K2 and Nitro use traditional radial sidecuts. Nothing fancy and very predictable, but if you ride in icy conditions on a regular basis you might lean towards the Rome boards as they should both have a sidecut with multiple contact points(at least I'm pretty sure). The camber portion in the boards will actually act as another set of contact points... Yay contact points!
About the Head boards... I really can't say as I've never encountered them other than as really crappy rental boards. Maybe those ones are better, but the ones I've been on were as close to being a plank of wood on the snow as you can get.
Lastly for bindings, try looking for last year's model of Burton Missions or Rome 390's for cheap... I often see them on clearance here in the US, but I have no idea about what's often in overstock in the EU.