>>16230485>One of those kits that’s inoculated already in a medium.Then that isn't spores. Those typically come in a syringe, but it's more common to buy LC syringes for gourmet. You likely bought a colonized sawdust block.
>Can I let them spore out and just continuously grow them?Yes, but you don't need to collect sporeprints to do that (though it's always a good idea to keep a library of prints). You can grow on agar from a clone (see picrel, it's cloned lion's mane colonizing grain and fruiting).
>When they spore do I have to worry about them spreading through the room and trying to grow on other stuff outside the medium?Potentially, if you have any exposed hardwood that tends to stay moist. I've seen oyster mushrooms growing out of people's baseboards.
Check out Philly Golden Teacher on YT, he can walk you through the basics of growing mushrooms (both actives and gourmets, the techniques are essentially the same).