I broke my wrist-triquetrum three weeks ago. How long would it take to fully recover?

A fracture in adults. Varies in what one would consider recovery based upon location , mechanism of injury , the nature of the fracture, soft tissue , associated injury, general health, associated conditions and many many factors. Average time for a nondisplaced fracture in a healthy adult is 6-8 weeks but full bone strength will be longer. There are times fractures r moved when stable even if not healed fully.
Depends. Is the fracture displaced? Do you have any associated ligament injury? Is it being treated with or without surgery? Any associated medical problems?
It depends. It is best to speak to your physician about the specifics of your fracture. Fracture healing time is dependent on the degree and type of fracture especially whether or not the fracture is displaced. Your overall health (concomitant diseases like diabetes etc slow healing) , age, nutrition, vascular status (smoking slows healing), hormonal health all contribute to fracture healing time.