There are a lot of exceptions to this, but mountain shoes will usually be SPD compatible (2 bolt holes), road shoes will usually be LOOK compatible (3 bolt holes). That only refers to the pattern of bolt holes in the sole. There are SPD-compatible road shoes, for example, and some shoes are drilled for both.

Online catalogs (and manufacturers' sites) will almost always tell you what hole pattern a given pair of shoes have or cleats need. Match them up.

For what shoes let the cleats hit the ground, read the comments above. That question's been answered three or eight times already.

There are some adaptors for matching incompatible cleats and shoes, but if you're buying everything from scratch, get things that work with each other out of the box.