Unfortunately you can't search for 3-letter words or less. I might look into that. However, searching for 'suction control valve' should provide the same results.
It could be the suction control valve but I'd grab a can of Liqui Moly Fuel System Treatment from Supercheap and throw it in. I've thrown in a full can with half a tank of fuel, haven't filled it with diesel, and it works superbly. You should see a result in 100-200km tops. Car will run smoother, won't 'hunt' or stagger at idle ... that's if the problem is in the fuel system. And it could well be, given that the lights remain on after the engine stops - indicating that it's likely to not be an electrical issue.
That doesn't mean you shouldn't check the battery. A poor battery can be a cause of issues, same as dirty terminals.
Fuel filters are painful buggers. Unless they're genuine, the central o-ring doesn't form a perfect seal. Now that doesn't mean the filter will leak - it sits high in the engine bay above the fuel pump which sits low on the right hand side of the motor. What does happen is the seal allows air into the fuel system and allows fuel to drain back to the tank making starting difficult. If this is the problem, you'll find the primer bulb will take more than 4-5 squeezes before it's firm. If yours firms up quickly, the fuel filter is likely to be good. It should be noted that even genuine filters must be aligned properly (and near perfectly) or even they can cause issues.
And for the record ... I am the only active admin here.