Your DS playing on his PlayStation all night is not on in any shape or form.
It's not only detrimental to him, it affects everyone.
Time to enforce some ground rules.
Turn off the router at a certain time every night. Or don't allow your DS access to the password, so you control it.
The key is to be consistent.
If you allow him to stay up all night, he's not going to stand a chance doing his GCSEs.
His laziness is also problematic, and it's hardly surprising if he's up all night.
No money or lifts etc., unless his room is tidy and dirty washing is put in the basket, otherwise it's not done. And stick to it.
I think your DP is unnescessarily getting a very hard time from some posters.
Constant sleep deprivation is a very effective form of torture in lot's of countries around the world.
Do not underestimate it's effectiveness for people to snap and lose control.
It's your DS that you need to get on track before it becomes an impossibility and now is the time to sit him down and explain what is expected of him and YOUR house rules, not his.