I have a question:

All the tabs on this site that say they are in the key of 'C', will they sound right if played with a different key of harmonica? (Besides it being just a 'lower' sound).

It really depends on the tab. There are those tabs out there that will have no problem being played in another key, but some tabs don't sound right when they are in the wrong key. The only way of really knowing is trying it out.