If River used all of her regeneration power to bring the Doctor back. Then does that mean she can no longer regenerate?

Yes River gave her regenerations away to save the Doctor so she can't regenerate anymore.
And when we see her "dying" in Forest of the Dead she is in the body we know. So she shouldn't regenerate again. But we could see some of her previous regenerations like melody for example (unlikely but...never say never).
As to why he would be with someone who would be dying on him: River might not be able to regenerate but a time lord body is more resilient than a basic human body (see Smith and Jones, The Unicorn and the Wasp...) and can live longer than a human even with only one body left.
But I did enjoy Rose/Doctor better too.

If River did use all her regenerative power to bring back the Doctor, she would not be able to regenerate herself again