1/B: It´s not posible this sentence... or are missing commas or missing words. Where do you find them? 2: (Y por qué nadie se preocupa por resolver el problema?) The sentence is perfect!!!!! The verb "preocupar" usually is written as: "preocupar + por/de"

#1B is wrong, maybe it was: "No he visto por que no se pueda" = "I don't see why not". as it would be a matching answer for A asking: "Do you really want to stay here?" #2 Is correct.

B: No veo por que no se puede.

2, Y por que nadie se preocupa por resolver el problema ? Is this a right sentence, can I leave out 'por' ??? If you leave out "por" it would still make sense but it would change a little, it would mean something like "so what? nobody cares about solving the problem?" instead of "and why nobody cares about solving the problem?"