You need spiritstone blocks to make spiritstone weapons. You make those at the same workshop as all your other stone blocks, though of course you'll need some spiritstones to start with.
There's a couple places on the world map that have one-time stacks of spiritstone blocks, if you're willing to go poke around, but that's not actually necessary.
"Food and cloth." As in, lotus root, wheat, flour, bread; cotton or woven fabric. Furs. Dried meat. Stuff that sells for a single spiritstone each, but that you can get lots of.
Generally I default to having the Inners on leisure as much as possible; high mental state is very important for breakthroughs, and can take a while to build up. (Note: you can temporarily raise Mental State over 100 with talismen, etc. If you do so, be careful about how low mental state has gotten before you take the bonus back off.)
Cultivation is pretty quick before Golden Core if you've made a proper cultivation array, so you can get that done pretty quick whenever, and manually pay attention to their mental state when you do it. After Golden Core you want to get cultivation progress by adventuring, not cultivating, so leave them on leisure.
You shouldn't be having disciples exercise for Inspiration at all; that's what outposts are for.
