You are correct. Either would be perfectly ok there.
Drivers________ speed laws only when they think the police are near.
a. obey b. observe
This one is more tricky, IMO. I think A would be used by native speakers. I think the distinction is that customs are created in the past, so we follow them. One can pursue a dream (or one's study as you said) because it is something that is ongoing or in the future.
No one needs to feel awkward in _______his own customs.
a. following b. pursuing
I hope I make some sense here.