Power chords are neither major minor diminished or augmented. These chords need 3 tones, a power chord or E5 chord only has 2 notes. E and B so it's more of an interval. In a E5 chord, E is the dominant pitch and B just strenghten the sound of E.

As for chords like Bm7. Yeah it's still a minor chord, the "7" indicates that an extension to the B minor chord has been added. If you take the B minor scale and count up 7 notes, you come up with the note A. Here's the notes, B, C#, D, E, F#, G, A. So a Bm7 chord is a B minor chord (B, D, F#) with the 7th added (A), together (B, D, F#, A).

An m or min after the note means it's a minor triad.
A capital M or maj means it's a major triad.
A aug or + means it's a augmented triad.
A dim or (small circle) o means it's diminished.

Any questions just ask. I'll explain any problems you may have.