This question is hard to answer with out more information, but it seems that you just have a very irregular cycle. You may want to go to the gynecologist and have some tests done or possibly go on birth control pills to regulate it.
No, there is nothing normal about having two periods in one month, by chance could you be pregnant. Just to be safe you should take a pregnancy test. It is common to have spotting or what is called implantation spotting early in pregnancy that could mimic a period.
No it is not normal, but things like diet, stress, physical activity, injury, disease can throw the cycle off. Also, not having a period for the month could mean pregnancy. Best to have a doctor check you out.
Periods may become irregular for various reasons. Medications, weight loss or gain, and activity level can all play an important role in this. Although this isn't exactly normal, any of these factors could have contributed.
