Yes, your period can come a week early. It is not all that uncommon because of the number of weeks in some months. Your period should come ever 28 days.
If you are on birth control such as the pill, it is possible to stop taking the medication a week early. This may force your period to come early, but it may just cause you to skip your period.
The timing of a woman's menstrual cycle is determined by numerous factors, and is essentially impossible to control with any reliability. Some birth control pills can affect having a period, or make it lighter than usual, but this cannot be done with any accuracy or certainty.
Yes, your cycles can come a week early, a week late, or you may skip a cycle all together. Don't be worried unless go more then six months without a cycle. Or if you seem to be having cycles less the 20 or so days. Your doctor can provide you more information.