Having a difficult time seeing the pic with the fork but it looks like the crown race (the black piece that fits onto the fork) is upside down but I can’t be 100% sure. The any crown race I’ve installed sits flat on the fork when installed.
There’s a specific tool, but that tool is basically just a pipe, so - yes. The pitfall to avoid is deforming the crown race on installation. Go slow and just tap it on. If it’s super tight I’d take it to a shop and have them set it for you.
I’ve never seen a plastic crown race that didn’t have a slot on it before, but first time for everything I guess.
Agreed -never seen a non split plastic one. I use Cane Creek headsets & had always used a length of PVC. Can’t remember exactly why but I bought the setting tool from CC & it works great.
Also, @Tim_87, I’d recommend some carbon safe grease on the fork crown where that race sits. It’s not totally necessary but will give you one less place to look when you’re trying to track down that deafening creak that’s driving you nuts!