Aphelion

I think you will find that stories that feature colonized asteroids generally choose larger specimens that are known to be fairly solid hunks of nickel-iron (fragments of the core of the failed or destroyed planet whose mass makes up the main asteroid belt). Then non-metallic elements would be mined from the carbonaceous(?) and other types of asteroids. (Given the presence of materials up to the transuranic elements on Earth, the rocky planets (i.e., non-gas giant types) probably have some traces of any element found on Earth. This would apply to the asteroid belt taken as a whole, too.)

If a nickel-iron asteroid isn't intrinsically close to being air-tight, tunnels could be sealed by melting the metallic ores or lining them with some advanced materials ("foamed" metals or plastics?)...

I think the asteroids with high nickel-iron content would be "stony" (viz. iron ore), whereas the carbonaceous(?) types would tend to be kinda crumbly (or am I thinking of comet nuclei?). There would likely be cracks and fissures even in a stony / metal-bearing asteroid that would require "caulking" to be airtight, but at least the damn thing wouldn't fall apart the first time you hard-docked with it.

I read a novel looooong ago in which some characters hollowed out an asteroid and bolted a drive unit into it and used it as a ship. I thought that was utterly cool.

Iskoday, you might enjoy "Mining the Sky," by John S. Lewis -- he writes about using asteroids as colonies, plus lots more.