How long will the upper front tooth take to grow after a child looses his baby teeth?

Age 6 To 8. "baby" teeth fall out usually when the permanent ones start pushing them out. Sometimes kids loose baby teeth for other reasons. Most lower and upper incisors erupt by age 6 to 8. There is also familial variants. As when parents got their adult teeth!
Depends . Sometimes you can see the crown of the permanent tooth when the baby tooth falls out. If this is so, then the tooth will start erupting immediately. If not, the tooth can take anywhere from days to a couple weeks. If the baby tooth was pulled by a dentist, it could take months to even years depending upon which tooth it was.
A few months. However if the gums are very fibrous it can take longer or may need dental intervention. We use lasers for this in my office.