There are two lines which have the number 0. Does that mean that I need to play two strings at once?
It means that you have to play the two open strings at once, followed by a hammer-on on the B-string only, while keeping the E-string playing.
More in general, any numbers on tablature that are immediately under one another should be played at the same time as a chord. The zero just says they should be played at the zero'th fret - ie the nut, which means play an open string.