Hi great questions:
1) Yes, the TAB is reflecting how the strumming pattern goes - anytime you see the low open E string by itself, it is played with a downstroke that closely follows an upstroke that's strumming the upper part of the chord. So there are a few strums in each bar that has an upstroke strumming the upper 5 strings then a downstroke that strums just the low string.
2) The G#min barre chord is an example of a barre chord shape with the root on the 6th string (low E string). With barre chords of this type, your index finger needs to at least hold down the note on the low string as well as the notes on the upper 2 strings. In this case, you also need to hold down the 3rd string with the barre finger. It doesn't matter if your index finger is cleanly playing the A and D string, since you are adding additional fingers to fret those notes.
So I guess my answer would be to hold down your index finger across the barre and make sure the notes on the 6th, 3rd, 2nd, and 1st strings are ringing clearly. Whether or not your index finger is actually fretting the 4th and 5th strings cleanly is irrelevant - it really just means to hold it down as comfortably as you can to get the notes ringing cleanly and clearly.
Make sense? Let me know how it goes!
Mike
Keep rockin!
Mike Olekshy
GT Guitar Coach