The importance of relationships may be why Boromir fell later on--he didn't really form any close relationships with any of the Fellowship in the book, and his attachments in the movie specifically excluded Frodo.
That is really well put. The loyalty to each other has to be stronger than the pull of the ring, or evil wins... Boromir never particularly bonded with Frodo, or the cause. His motives never ceased being his own agenda, and followed the fellowship only so far as the mission followed his own.
I have a feeling Sam, Merry and Pippin have no particular commitment to the mission, but a deep commitment only to their friend. Frodo is safest with them. They have no personal ambition for evil to get a foothold in.
Aragorn, on the other hand, felt duty to the mission, and perhaps a personal bond with Frodo. His will is strong, but his mettle could perhaps be more tested than the others because of his ambition.
The weaknesses that could have been exploited in Legolas and Gimli are unknown.
I'm sure that's right. Personal ambition for power is so rare in the Shire that they don't even need a government.
Still, the ring does have the capability to awaken desire for power in hobbits as is shown by Smeagol/Gollum and Frodo and Sam later.