AS a beginner I have a question to you, When I play B Major(Must I catch all strings on fret 2 with my one left finger?)as you show at the below image
Unless the chord is notated as B/F# you really don't need to worry about the 6th string (fret 2 = F#) which can (or maybe should?) be omitted from the chord.
The most important note to fret cleanly is the D# on the 2nd string fret 4 because it is the only note that is not doubled.
Even if you only play the 2nd, 3rd and 4th strings fretted at the 4th fret it is still a B major chord but not in root inversion (actually 2nd inversion = B/F#).
Adding the B on the 5th string/2nd fret puts the chord in it's root inversion and adds a satisfying bass note.
Adding the F# on the 1st string/2nd fret will change the sound of the chord but is completely optional depending on which sound suits the music best.