Welcome.
There are a couple of ways of working out the SC's earned. It would be much easier if Qantas actually allowed searches to occur for non-Qantas flights through their SC calculator
https://www.qantas.com.au/fflyer/do/dyns/initialPointsEarned
Something to keep in mind. When dealing with International flights, only 'Y' class fares earn "Economy" status credits. Other classes in Economy earn "Discount Economy" status credits. Premium Economy, Business and First are treated differently, but not relevant to your question as you are in Economy for all legs. The official Qantas Blurb is:
"# For domestic flights within Australia, Full Economy includes Fully Flexible (classes Y, B, H) and FlexiSaver (class K and W). For international flights, including domestic flights within New Zealand, Full Economy is class Y. For travel on oneworld alliance or Air Pacific, Full Economy is class Y. For flights on Jetstar, Full Economy includes travel on Jet Flex fares. For flights on British Airways, Full Economy includes travel on World Traveller Plus fares. If you fly on a Flight Upgrade Award you will receive Status credits for the fare class originally purchased."
Ok, that out of the way, I suggest you review the "Airline Earning Table" here:
Frequent Flyer - About the Program - Terms & Conditions and ensure that your flights earn SC's. ie "Status Credits are earned on all eligible booking classes" is written under your airline and that the classes are eligible classes for earning SC's. Read the various conditions carefully - especially when codeshares are involved.
You can use the "Great Circle Mapper"
Great Circle Mapper , plug in your trips (eg MAN-LHR), then get the mileage and compare to
Frequent Flyer - About the Program - Status Credits for the number of SC's earned. If the mileage returned is pretty close to the cut-offs for each band, then you might get either of them as the mileage used is determined by Qantas/partner airline.
Another way of checking (easier) is to use Mileage Monkey
MileageMonkey 0.95020 , Ensure "Earning Preference" is set to QF (Default setting), enter in the city pair (eg MAN-LHR) in the "Oneworld Explorer Validator" field, tick the box "Ignore Errors" and click the "GO" button. The number of SC's earned will be shown down the bottom of the page. "Econ" is actually "Discount Economy" - double it if you are in Y class. Business and First are correct. Note again, that the results shown may be slightly out if you are on a flight that is close to a band change in the Qantas scheme.
Hope that helps. My calc's for your trips:
MAN-LHR - 10 sc's.
LHR-SIN 40 sc's.
SIN-DPS 25 sc's
DPS-MEL 0 sc's (due to the stupid marketed by Qantas, operated by Jetstar rule in the T&C's earning table)
So you should make Gold on your SIN-DPS flight.
