The 7th chord is considered a bar chord, which means you can move it anywhere. You can use the same formation and just slide it up the neck.
Whatever your index finger is playing, it the name of the chord. E.g. 1st finger (index) on the 5th fret is A, therefore the A major 7.
The chord is called a 7 because you play the 1, 3, 5, and 7.
The difference between a minor and major 7 chord is that in a minor the 3 and the 7 are flat. You can also take the minor 7 up and down the neck in the same formation.
A dom 7 or A7 = dominant 7 chord, it’s a major dominant chord with a flat 7. This is where the blues feel comes from.
To make this a minor 7 chord, all you do is lift up your 3rd finger
You will start to find that some chord sound really good open - B minor 7 sounds really cool instead of barring it, but c sharp minor chord sounds weird, so bar it.
Once you learn these bar chords you can start playing some really nice picking patterns.