How long after your period could you get pregnant?

It depends. Depends on many factors. Take a 28-day cycle and count from the first day of bleeding: you are 'at risk' to become pregnant as early as the 9-10th day, but more usually between the 12th to 15th. In a shorter/longer or irregular cycle, it will be different. Do you want to conceive or are you asking how to avoid pregnancy? The facts are the same but the strategy would be different!
Varies. Some women may ovulate as early as 5-7 days after day 1, which is the first day of menstrual flow, not spotting. Usually though a person ovulates 12-16 days prior to there menses.