Real world physics are different from Nirn, they do not apply where magic and dragons churn about. And actually, patching up the sun will basically remove a very large hole from mundus. Which is better than the dawnguard's option. Magnus's whistle will no longer allow as much aetherial magicka to seep into mundus, a bad thing to some, a better option for others. The streaming amount after such an event should be equal to what the ayleids harvested within their wells, smaller but still prevalent. For the stars will still be within the night's call, as they are smaller rips into aetherius. Giving those few mages left some source of power.
All life would definitely not be extinct. The aedra operate independently from Magnus's gate, the sun. Kynareth will still be around, Arkay will still be around, Akatosh will still be around, Dibella will still be around, Mara will still be around, Zenithar will still be around, Stendarr will still be around, Julianos will still be around. They support mundus, as long as they are still around, all will be alright. So the argument of 'no sun, no life' is as void as Sithis.
What a load of old twaddle!