I have a leaky roof. Do I need a new roof?
Not necessarily. Roofs leak for many reasons besides shingle failure. Hire a professional to fix the leaks and give you an analysis of the overall condition of your roof.

Do I have to tear off the old roof before putting on a new one in North Rim, Arizona?
That depends on how many layers of roofing are already on the house. In general, it's a bad idea to have more than two, although some types of light-weight metal roofing can cover just about anything.
How long does it take to replace a roof? Depending on the type of roof, it can take from a few two days to 3 or weeks.