Zanpakuto Type would fall either into Kido or Light. It's really up to you to your discretion as there are Zanpakuto in the manga that have no definitive
'type'. District wise, whatever you feel best fits your clan. 50th and beyond is where life gets extremely rough. In essence, the lower the number the better the living situation.
As for abilities, maybe think a supportive ability. Maybe a flashbang ability that uses light to blind enemies, or creating a construct out of light that fights for you. Skies the limit, my friend. There's also zero shame in drawing inspiration from other
series.
Seinaru kainyū no tate: Shield of holy intervention. If this is a simple defensive ability, that blocks attacks
within reason, then a ten-post cooldown is excessive unless you intend for that. Otherwise, you may tone it down to 5 or 6.