Why are white and black about evenly matched in this position.
@1
"Can't the black easily win the d4 pawn (after Re8 to protect the bishop)? "
++ No. White can always save the pawn.
"attack the bishop with the pawns in front of my king"
++ Yes: 11 h3 Bh5 12 g4 Bg6 13 Bxg6 hxg6 14 dxc5 Bxc5
"common advice to beginners" ++ What advice? Both sides have castled king's side. White can play h3 and g4. It were different if black had castled queen's side O-O-O or not yet castled.