No, the calculating your own tax thing was under the old system where you had until January to file your return on paper, but if you didn't file it by the end of October (or was it September?) you had to calculate it yourself.
Online filing calculates automatically whenever you do it - that is one reason they are so keen to get everyone to do it.
Refunds of overpaid tax for the previous year generally come through within a fortnight, often within a couple of days. If the refund is due to a reduced payment on account for the current year it can take a little longer.