I haven't done Kallitypes, but I have done quite a few van Dyke prints.
I use a very cheap brush - a pack of ten cost the equivalent of $1.80 in the supermarket. So I got brushes for salt prints, cyanotypes and van Dykes at the same time - and when they get too grubby, I throw them away. There's metal on them - that doesn't matter. It's only a potential problem if the metal is rusted.
I use one single tray. Wash, dump, wash, dump, fix, dump, wash. Kallitypes must be developed and cleared too, AFAIK. Still doable in a single tray.
A density range of log 1.8 is a lot of contrast. A "normal" negative for enlarging has something like log 0.6! I don't use a densitometer, so I can't really help you there. But in my experience van Dykes need a lot less contrast than that, log 1.8 is far up in POP/albumen territory!
Kallitype can be considered as the silver version of platinum/palladium, and similar contrast controls are available. Someone else will surely come along soon with a proper explanation.
To make things easy on yourself, why not start out with van Dyke? Much simpler, very similar result, and then you'll learn a lot of the basics before moving on to more complex processes like Kallitype and Pd/Pt.