Regarding fretting the B chord, when you say the 1st string, do you mean the high E string or the low E string?

If it's the high E string, you actually could bar your index finger all the way down the 2nd fret so that F# note could ring. But usually, you are barring the 4th fret with your middle or ring finger, so you could curl that finger so that it dampens the high E.

If it's the low E string, use the tip of your index finger to dampen it. Yes, you will still get that slight thud when you use full strums, but practising to not even pick that string really helps too. After awhile, you won't even have to think about it!

Thanks for the great questions Ron ... keep pickin'!!
Mike