I have a few situations regarding fasting.

1) I recently learned that with fasting, I should’ve taken the earliest calculation method. Because I didn’t, is my fast invalid?

2) What about imsak time? If one does not begin his fast by that time, but rather by the time of Fajr Azan, is the fast valid?

1) No, you don’t have to take the earliest calculation method if it’s not proven to you that it’s the correct method. So your fasts are valid.

2) Yes the fast is valid. Imsaak time is based on precaution.