When the cause of a root canal infection is solved, does bone regrow at/near root tip in the space that the infection laid in? how long may it take?

Yes: Bone will regrow in the defect. Depending on the size of the defect, it can take a few months and even up to a year.

Yes: It depends on many factors. A complete medical and dental history and exam is necessary. Under normal conditions, the bone will fill in after the source of the infection has been eliminated. The time is also dependent on several factors, but the bone can regrow after 6 months in many situations.

Root canal healing: When a root canal has been completed and the canals are sealed to remove the source of nutrients for the bacteria, studies have shown that regeneration of bone at the apex of the tooth occurs and 71% of the lesions in the bone have complete resolution within one year on average. While some lesions do not heal on their own, surgical intervention can usually resolve this problem.