Banshee's veil may be useful as well to prevent people from stunning you after you start channeling Death Lotus.

I find Deathfire more usefull yes, though more expensive.

If you want some life back, start with a Doran's Shield and keep it while you don't have the Will of the Ancients (this last one gives an awesome heal during your ulti against many people). Anyway, i'd start with the ring and throw it after when needing a slot, i don't think Kata needs regen when played AP (make the WotA only if you really want leach or have nothing else to do, there are far better items to get before). The CDR is great but Kata's CDs already are really good (not to mention your ulti have a great CDR when you get a kill).

If oponents have heavy physical dps, maybe a frozen heart could be worth the price if you really want CDR (i'd rather go thornmail, cheaper and adding a little dps output).

And yes the 20% is pretty useless. If you don't think you need this item, I'd recommend Deathfire Grasp for the Ability Power and Cooldown Reduction. Just as cheap, but you'll lack health regen. Play extra cautiously.

It's really for the cooldown reduction. But the regeneration helps while your farming lanes + it's pretty cheap for what it provides. Considering Katarina's abilities are free to use, cooldown reduction is extremely useful for her and necessary.

Spirit visage ? Why ?

I'd understand a Will of the Ancients, but the visage is fully useless ... you don't have heal nor leach nor regeneration, what will you do with 20% more of nothing ?