How did the monks know that Isabelle's fiancee stole the beans?
Erm, they saw him?
Jack's locket was air-tight? The bean was in it when he went underwater.
It's not very far-fetched for a locket to be air-tight. Many are, and can keep even pictures dry when people swim wearing them.
The film implies that Jack's world is our world, so how do the Astronauts and airplane pilots not notice the land of giants?
That's an easy one: it's the same reason people don't see it in the sky on a cloudless day. The beans were made with black magic so it seems likely that they are effectively acting as a bridge between two different worlds.
Another theory: maybe they did find the giants again, and, with much more advanced technology, obliterated them and kept it a secret from general public.
Why, after they were freed from Roderick's influence, did the giants decide to go to war with the humans anyway? They seemed to have no interest in doing so before then, nor did they act particularly pleased when first ordered to do so.
They thought they could win this time, maybe, seeing as they only lost the previous human-giant war because a human took control of the crown that took control of the giants. With a giant in control of the crown that controls the giants...
The giants were always interested in invading the human lands again because they're greedy as hell and humans are delicious. But they were prevented from doing so by the lack of a beanstalk (remember, it was the monks who grew them, not the giants). Plus, even if they could grow a beanstalk, there was Erik's crown to worry about.
Why in the world was Isabelle engaged to Roderick in the first place? Not only does she make it clear she's not happy with the idea, but Roderick doesn't seem to have any notable reason why the king would think it'd be a good idea to force his daughter to marry him. Yeah, Isabelle had to marry nobility, but surely there were other options besides him?
It was mentioned that he held several government positions, and he might have been a competent (albeit evil) administrator. Maybe the king wanted a son-in-law with proven kingdom-ruling credentials?