How did the Earth survive before The Doctor rebooted the universe?

Question

I have found multiple conflicting collapse of reality situation due to explosion of TARDIS.

From The Pandorica Opens episode transcript:

WHITE: The cracks in time are the work of the Doctor. It is confirmed.
DOCTOR: No. no, no, not me, the Tardis. And I'm not in the Tardis, am I?
WHITE: Only the Doctor can pilot the Tardis.
DOCTOR: Please, listen to me!
WHITE: You will be prevented.
DOCTOR: Total event collapse! Every sun will supernova at every moment in history. The whole universe will never have existed. Please, listen to me!
CYBERLEADER: Seal the Pandorica.
DOCTOR: No! Please, listen to me! The Tardis is exploding right now and I'm the only one who can stop it! Listen to me!

From The Big Bang episode transcript:

RORY: What are you doing?
DOCTOR: Looking for the Tardis.
RORY: But the Tardis exploded.
DOCTOR: Okay then, I'm looking for an exploding Tardis.
AMY: I don't understand. So, the Tardis blew up and took the universe with it. But why would it do that? How?
DOCTOR: Good question for another day. The question for now is, total event collapse means that every star in the universe never happened. Not one single one of them ever shone. So, if all the stars that ever were are gone, then what is that?
(A large burning ball in the sky.)
DOCTOR: Like I said, I'm looking for an exploding Tardis.
RORY: But that's the sun.
DOCTOR: Is it? Well, here's the noise that sun is making right now.
(The Tardis noise.)
DOCTOR: That's my Tardis burning up. That's what's been keeping the Earth warm.

Exploding TARDIS took place of our original Sun to keep the Earth warm. But, these two quotes from transcript says, our original Sun either went Supernova (which isn't possible in real world due to inadequate mass) or never even existed. Both looks conflicting, but in either of case, how could the Earth survive? Sun's Supernova can easily kill Earth and if our Sun never ever existed, Earth can't come in existence (in case you are thinking about Earth revolving around the exploding TARDIS since beginning, it's also not possible as heavy elements to form a planet are only forged in the heart of a heavy star, not in the heart of exploding TARDIS which was keeping River Song in time loop).

Answer 1

The Doctor vaguely hand-waves the issue away by saying "Eye of the storm, that's all. We're just the last to go out."

(This type of explanation actually pops up a few times during that season to explain the way the cracks in time are working -- that some temporal event or catastrophe has an "epicenter" and the nearness to that point affects how your are affected by the event.)

In this case, what it seems The Doctor is trying to say is that the effects of the TARDIS explosion radiated outwards in all four dimensions from the exact point in space/time that the explosion happened. The regions of space/time closest to the TARDIS at that point were being "held intact" by the TARDIS's presence, while the regions further out were collapsing inward.

In effect, the Earth's sun both ceased to exist and collapsed into a white dwarf simultaneously (note: our sun will never go supernova - it isn't big enough) at the moment of the explosion, and the effects of that change are working their way forwards and backwards through time and outward through space, but away from the TARDIS. The Earth hasn't noticed yet because it's closer to the TARDIS than the Sun.

As the collapse continues, I presume the bubble of safety around the TARDIS will shrink, and the effects of all the external changes will continue to move inwards until it, eventually, reaches the TARDIS itself and the universe goes away.