Dominants are always major. In c minor, the bflat is raised 1/2 step to b natural because it is the leading tone. In the case of f minor going to c major, you can view it two ways. First, you are playing the subdominant (f minor) in a c minor tonality and resolving to c major. Raising the 3rd in a minor key at a cadence (most usually at the end of a piece) is referred to as a Piccardy third. The second way of looking at it, if you are in c major and there is a f minor chord, it is called "modal borrowing", because you are "borrowing" from the minor mode.
Take C minor triad, then go to G major, this is not part of the C minor scale
That's where you're wrong. It is part of the harmonic and melodic minor scale.