Which sentence is correct?
1)

A) One of the pilot's responsibility is to ensure that the plane's engines work well.
B) One of the pilot's responsibility is to ensure that the plane's engines are working well.

2)
A) Are dinosaurs still living now?
B) Do dinosaurs still live now?

3)
A) I just try to guide their thinking through some interesting questions and activities.
B) I just try to direct their thinking through some interesting questions and activities.

Question

Which sentence is correct?
1)
    
    A) One of the pilot's responsibility is to ensure that the plane's engines work well.
    B) One of the pilot's responsibility is to ensure that the plane's engines are working well.

2) 
    A) Are dinosaurs still living now?
    B) Do dinosaurs still live now?

3) 
   A)  I just try to guide their thinking through some interesting questions and activities.
   B)  I just try to direct their thinking through some interesting questions and activities.

Answer

#1 both a and b are correct and well as #2 a and b.  #3a is correct but b is not correct for a teacher with the choice of the verb "direct" since it could be taken as administer, manage, supervise, command, order, etc., being then improper for the context of a teacher.

Answer

1A and B should both say 'one of the pilot's responsibilities...'. As for the verbs at the end of the sentence, both are acceptable, but B sounds better to me.
2A and B are both acceptable, but A sounds more natural.
3A and B both sound fine to me.