I have seen everywhere that mac users simply put textures and stuff into the q3 folder, for use with Radiant, (which I have downloaded) but what if we don't own quake 3?

Can we still map, and set up radiant, like on a windows computer?

I found a file download for a folder called 'nexuiz-radiant' but it's for windows, and aparently makes mapping possible without quake 3.

You don't actually need q3, you just have to adopt it's directory layout. Afaik it is possible to create maps on osx, but setting up gtkrasdiant is a pita, since there are only old 1.4 builds for mac, which don't have builtin nexuiz support like 1.5 (perhaps someone here could make a 1.5 build for mac...).