Had last period beginning feb 1st. My period just began again today, feb 28th. Is this abnormal?

Not necessarily. Women have different cycle lengths. Anywhere from 25-30 days is typical. As long as you have the same cycle length each month i wouldn't be concerned. Your cycle length for february would be 27 days.
No. The average number of days between the start of one period and the next is 28 days, but normal can vary from 23 days to 32 days.