DFirst1

Question: Why was Boromir allowed to join the Fellowship of the Ring? Since he is vulnerable to the Ring's corruption.

DFirst1

Chosen answer: Virtually everyone was vulnerable to the Ring's power to some extent, even Frodo Baggins. Frodo's purity of heart and incorruptibility made him the least affected by the Ring and made him the only logical choice to actually carry it for the duration of the mission; but EVERYBODY was vulnerable to its seductive power, some just more so than others.

Charles Austin Miller

But prior when the Fellowship was formed, he was tempted by the ring. He even tried to convince the council that bring the ring to Gondor would destroy Sauron. So why did Gandalf or Elrond accepts Boromir as a member of the Fellowship?

DFirst1

Well, Boromir's younger brother, Faramir, would probably have been a better choice for the Fellowship, if he had been available. But Faramir wasn't available and Boromir was. Boromir also wasn't actually "chosen" for the Fellowship, he simply went along out of loyalty to Aragorn. Gandalf and Elrond may have suspected Boromir's weakness (possibly even as a threat to the Fellowship), but Boromir was a seasoned warrior whose skills in battle would be valuable on this incredibly dangerous mission. Also, you may recall that Boromir wasn't even nearly as weak or unbalanced in the actual Tolkein story; rather, director Peter Jackson made Boromir more of a loose cannon in the film, which is not how he was portrayed in the book. In other words, Jackson wanted an even more unbalanced element threatening the Fellowship from within, so he amplified Boromir's weaknesses.

Charles Austin Miller

Question: When the Fellowship are on the side of the mountain and arguing about which direction to take, Gandalf says "Let the ring bearer choose". Why does Gandalf say that? He knows that Frodo has enough on his plate, what with taking the ring all the way to Mordor, so why add to his problems by making Frodo decide the way to go?

Answer: Because, like it or not, he's the leader of this quest. Gandalf is only a guide; Aragorn, Boromir, Legolas, and Gimli are Frodo's guardians, while the other three Hobbits are simply companions. Besides, Frodo's the one carrying the increasingly burdensome ring. If he thinks one path easier than another then that's his call.

Phixius

Answer: Because he is the ring-bearer. Frodo must decide on where the ring could take safely take them.

DFirst1

Answer: Gandalf is the leader of the fellowship, therefore he must decide the group where to go and what course of action takes place next. Frodo is just the ring bearer not the leader of the fellowship.