I usually get an email from them to tell me that I have won a prize. You can get it paid into your bank account or reinvested and paid into your premium bond account.
No, NS&I will send you an email or text. Of course you can check online from the 2nd of the month (or the 2nd working day of the month) if you can't wait.
Yes they will. You don't have to do anything. I was informed by email that I had won a prize in the November draw, It turned out to be £100 which stopped me removing my savings to put them into an account offering a lowish interest amount.