At the end of The Parting of the Ways, after The Doctor takes the time vortex energy out of her she passes out, and when she wakes up in the Tardis she remembers nothing about how she became Bad Wolf and defeated the Daleks, and for some reason the Doctor decides not to tell her.

But in the Series 2 episode Doomsday when she meets the Daleks again, she tells them about how she met the Dalek emperor and vaporised him. So does she remember or did the Doctor just fill her in?

Probably just remembers, just some temporary memory loss i'd imagine.

I would say that the Doctor probably filled her in.

In Parting of the Ways, she didn't know what had happened, all she could remember was 'singing' in her head.

Deleted.

Another question can The Heart of the TARDIS be opened up again Rose said she couldn't because it was like forbidden or sealed, and will it have the same effect if you look into it giving someone the power to control Life or Death?

Is the heart of the ship even in the same place or was it relocated?

It's practically left to the viewer's imagination what the Heart is/was, or what it could do - it turned Margaret Blaine into an egg for some reason. And if it can turn a human or Time Lord into a Dalek-kliing powerhouse, wouldn't it be worth the cost of regeneration - why didn't the Time Lords use it as a weapon?

Maybe they didn't know the full reaches of its power, maybe we know less than we think about the TARDIS. Or it could be that no one knows if it will have the same effect.

You would think someone would be willing to simply regenerate to kill every Dalek.

Particularly if it's possible (although not common) to simply grant a new cycle. Send one Time Lord out armed with a Heart and a million regenerations - it'll take less than a Moment.