How long do Bilbo and Gandalf stay at Rivendell?

Answer 1

According to Appendix B-The Tale of Years from The Lord of the Rings, Frodo left Bag End September 23, 3018 of the Third Age.

Frodo reached the Morgul Road at dusk on March 9, and passed the Crossroads and Minas Morgul the next day. On March 13, he was captured by orcs and taken to the tower of Cirith Ungol, a tower in the Ephel Duath (Mountains of Shadow), the mountains that bordered Mordor to the West.

Frodo and Sam escaped from Cirith Ungol March 14, 3019, and began their journey along the Morgai, the smaller mountain chain behind the Ephel Duath. Three days later, on the 18th, Frodo had crossed the Morgai, and was caught on the road to Udun in the north of Mordor.

So it depends on where you consider Frodo to have entered Mordor. If he reached Mordor March 10, when he passed Minas Morgul, it took 5, 30 day months and 17 days. If he reached Mordor March 13, when he was taken to Cirith Ungol (or before that, on 12th, in Shelob's lair), it took 5 months, 20 days to reach Cirith Ungol, and 5 months, 22 days to cross the Morgai.

Answer 2

The exact length of time is not known, but the chronology indicates that the two of them fought for ten days. Gandalf fell at the bridge on January 15th and cast down the Balrog on the 25th. As Gandalf said, 'We fought far under the living earth, where time is not counted.'

Answer 3

The journey from The Shire to Mount Doom took six months.

Answer 4

According to The Hobbit, it hung down below his waist.

Answer 5

14 days