Is it true you need a certain technology to get a master builder? If so which technology is it?

No, the Village Tech does not affect a villager's skill. To get a Master Builder, you need to have them working on construction projects, fixing huts, or you can make them exercise (using a certain stew) and they will sometimes gain building skill.

Does it take longer to gain building skill from fixing huts rather than building them?

Usually they'll succeed or fail in fixing a hut then go off to do other things. They need to be dragged back to work all the time. If they are actually building them, they'll carry on doing so until it's finished. So yes, it does take longer to gain skills. However, when they are building, they have to walk long distances fetching wood and rocks, so it takes quite a while for them to complete each individual task.