How long does it take for precancerous cells in your body to become cancer?

Varies. You start acquiring the mutations that produce cancer when your life starts. Cells that a pathologist can tell are "precancerous" signal "time for treatment". Cases in which the mildest of dysplasias of the cervix have turned to invasive cancer in less than a year are well known. Others simply disappear, or never progress. Be glad for early detection -- and congratulations on a likely cure.
Maybe never. Every cancer has it's own growth rate which we define as it's "doubling time" (how long does it take for the cancer to double in size). Some pre-cancerous cells never have the ability to transform into invasive cancers, however that is probably the exception rather than the rule. Was there a specific type of cancer you were referring to?