You can, but you will want to remember to turn off the cab sims on your preset, as the katana's speaker will be your "cab". I've done it before using my Katana Head into a Marshall 412, and it was pretty killer.
if by intonation you mean the tuning between a string up the fretboard, no... there is not way to affect that with the Helix, b/c it is a physical thing about the relationship between the neck/body/bridge/ect.
it works, but the issue you may be having that it is kind of picky as to which IRs it can load.
There is a website called LiveReadySound that sells a pack of IRs made specifically for the PC, and they are pretty good. Might be worth checking out.
Yep. I do it fairly often. You'll have less "oomph" on the bass end of things than you would with an amp designed specifically for keys, or with a PA, but it definitely works
Experimentation is your friend. I usually do comps first, then dirt pedals, then amp/cab/ir, then delays, mods, reverbs last. But, you can switch that order around and get some cool effects too.
I went with the LT, I have no regrets. The only thing the full floor has that I would have had much use for is the mic input, fixed that with a cheap $50 mixer.
I would say that the PC+ is definitely worth it. I picked one up a few months ago, and it is amazing. The Flat mode works great for an FRFR solution, and the Speaker Emulations are awesome too. The ability to load IRs into the PC+ is awesome as well.