I'm curious to know how could I play the minors and the 7th chords using the power chords.
Can I assume that you're starting from the assumption that you can replace a power chord with a major chord?
If I'm right, ask yourself - why do you think that? It's not usually the case that a power chord sounds exactly like a major chord built on the same root note. So we're not using a power chord because it is a way of playing a major chord - we're using it instead of a major chord.
If a song has a chord progression C - C - F - G (all those chords being major), and instead we play C5 - C5 - F5 - G5, then it doesn't sound the same. However, you still have a sense of the same harmonic movement that the original chord progression has. So the power chord version will 'work', and be recognisable as the same song if you sing the melody over the top.
Now, let's consider the chord progression C - F - G - A minor - F - G - C. What happens if we decide to play C5 - 5F - G5 - A5 - F5 - G5 - C5 as a substitute? It's possibly subjective, but to me it's a similar result as before : The A5 power chord works fine as a substitute for the A minor chord, and in fact in my head I hear it as a minor chord, possibly due to my expectations of how harmony works in C major. So (subjectively) you can use power chords as a substitute for minor chords.
What about sevenths? Well, try playing a song with this variation of the 12-bar blues progression:
C F C C7
I wanna play the blues, but I only know the power chords
F F7 C C7
Yeah, I wanna play the blues, but I only know the power chords
G F C G7
Well, that root and that fifth is all my stiff little fingers can afford...
Now try playing (and singing!) it with just power chords - C5, F5, and G5. Does it sound the same? Again, no. Is it recognisable as basically the same harmonic motion and song? To a large extent, to most listeners, yes I think it will be. So again, you can use power chords as a substitute for seventh chords.
Is it possible to play the minors and 7ths differently(producing distinguished sounds) using power chords, or do all the variations generalise into a single power chord?
Simplistically (and somewhat subjectively) speaking, you're on the right lines when you say they generalise to a single power chord. That doesn't mean that a power chord is just the same as (or as good as) playing a major, minor, or seventh, but in many contexts, it will do the job in the context of a song.