Does vomiting and unintentionally swallowing some of it while asleep and then waking up invalidate the fast, and does renewing the intention for a voluntary fast after sunrise compensate for this mistake?

As long as you swallowed something unintentionally, your fast is not broken by that. As for a supererogatory fast, it is permissible to form the intention during the day for someone who has not done anything that would invalidate the fast. Renewing the intention has no effect on the validity of the fast; either it is valid, in which case there is no meaning in renewing it, or it has become invalid, in which case there is no benefit in renewing it.