Can anyone tell me if you are allowed a stopover in Singapore for this journey should you book an award ticket using krisflyer miles?
Yes, you are allowed one free stopover on a round trip saver level award ticket. You can pay (I think) US$100 for a stopover on a one way saver level award.
Not sure in either case if you can pay another US$100 for another stopover, which in your case would be NRT, or SIN in both directions.
One further thing - if you book a return award ticket with Singapore, you automatically are entitled to one stopover and this can be booked on their website.
You can add a second stopover on a return ticket, but this must be done over the phone.
If you call their contact centre to make a reward reservation and are adding a stopover, don’t forget to request the 15% discount because you are unable to book the stopover online. you will get the 15% discount once all of your travel is on Singapore Airlines. If any part of your journey involved a Star alliance/other partner, you won’t get the 15% discount.
Is the free stopover on both inbound and outbound flights I.e. Could I do Sydney - SINGAPORE - LA - SINGAPORE - Sydney?