Programmes are supposed to recognise people who have joined a second time (generally after a number of years gap) and so transfer the miles to the new/active account.
From experience, miles are generally awarded within 2 working days of taking each leg of a journey. Plus, I know from experience that if you pay for a flight, but don't take it (or cancel it) you don't get the miles!
P.S. I did SIN-LHR yesterday on SQ and the service was impeccable. Puts all European & North American airlines in the shade and positively burries some supposedly 'full service' carriers!