How old was Obi-Wan when Qui-Gon-Jinn took him as an apprentice? What age? And how long was Obi-Wan his apprentice?
He was 12 years old and served 13 years as an apprentice
I took the following excerpts from the Kenobi Star Wars Wikia page.
It wasn't easy to read his age out, but as the side listed his life in chronological order, you can read it between the lines.
At first, Kenobi had bad luck being a Jedi Scholar, because ...
Despite his rapid growth as a Jedi, by the time Kenobi reached the age of twelve, it seemed that his chances of becoming a Jedi Knight had all but passed him by; Younglings who weren't selected to be Padawans by the age of 13 would be shifted into one of the divisions of the Jedi Service Corps.
Qui-Gon Jinn visited the Jedi Temple and Kenobi took one of his competitors to show how good he was fighting. Jinn found his attitude a bit too rough and went on. Bad luck for Kenobi.
Kenobi was sent to the mining colony of Bandomeer to work as a ploughman for the AgriCorps. Strangely enough, Jinn happened to be sent on a mission to the same place.
This event was a trap for Jinn and as they worked together, Kenobi and Jinn survived.
But again bad luck for Kenobi, as Jinn only sent him to another mission referring to the same enemy. But ...
During their altercation with Xanatos, Jinn discovered Kenobi's true potential, and took him as his new Padawan learner.
After that, the article described the early stages of the apprenticeship and that they got a little dispute. The next chronological named event was his 13th birthday:
For his thirteenth birthday, Kenobi received a river stone from Jinn, something that came from the River of Light on the Jedi Master's homeworld.
So Kenobi wasn't taken as an apprentice at 12 years old, became one and on his 13th birthday the next event happened. Kenobi was 12 years old when Qui-Gon Jinn became his master.
Now to his years as being an apprentice, we can calculate that quickly.
He wasn't apprenticed-out correctly, as his master was slain by a Sith Lord. This event happened on the
Blockade of Naboo (32 BBY)
which is also the story of Star Wars Episode I: The Phantom Menace. He was born in 57 BBY and his master was slain in 32 BBY, meaning that Obi-Wan Kenobi was 25 years old when this happened.
As he was taken as an apprentice at 12 years old, we can say that he served (25-12)=13 years as an apprentice.
Using only strictly canon sources, starwars.com's entry on Obi-Wan tells us only that Obi-Wan was in his teens when he became Qui-Gon's apprentice (we don't know a more exact age):
According to an archived blog entry on starwars.com written by Leland Chee, Obi-Wan was born in 57 BBY and Episode I took place in 32 BBY. Assuming Obi-Wan was about 13 when he became Qui-Gon's apprentice, that means Obi-Wan was Qui-Gon's apprentice from about 44 BBY to Qui-Gon's death in 32 BBY (about 12 years).
Obi-Wan was 12 when Qui-Gon took him as a Padawan. Here's the story from Wookieepedia:
Despite his rapid growth as a Jedi, by the time Kenobi reached the age of twelve, it seemed that his chances of becoming a Jedi Knight had all but passed him by; Younglings who weren't selected to be Padawans by the age of 13 would be shifted into one of the divisions of the Jedi Service Corps. One day, Jedi Master Qui-Gon Jinn visited the Jedi Temple to watch the matches. Kenobi dueled one of his competitors, Bruck Chun, to draw the attention of the maverick Jedi Knight. Kenobi fought valiantly to the point of exhaustion. The final offensive against Chun was carried out so fiercely that Jinn thought Kenobi too dangerous and declined training the boy. Kenobi was sent to the mining colony of Bandomeer to work as a ploughman for the AgriCorps. Strangely enough, Jinn happened to be sent on a mission to the same place. The youngling and the Jedi Knight had to work together if they wanted to survive the mission, which was a trap set for Jinn by his former Padawan, Xanatos. Kenobi showed Jinn that he was worthy to be taken as a Padawan learner.
He was 25 when Qui-Gon died from the duel with Darth Maul and took Anakin as his apprentice, so he spent about 13 years as an apprentice.