No. You should have one period a month around the same time each month. I suggest you go to your doctor and have him give you his opinion. If this has happened before it's a good sign that something is wrong.
It is completely normal to have irregular periods for the first few years after you first get your period. If it has been going on longer, talk to your doctor.
Yes its absolutely normal it happens to a lot of women as some have more activeness but there isn't anything to worry but you can consult your doctor if you are feeling insecure.