some more questions about cauldron haze and persist vampire hexmage wither magic

[Person4561]

if you use cauldron haze on a creature then when it persists you use vampire hexmage to remove the counters from the creature, can you again use a cauldron haze to make it persist again?

If a creature has wither damage on it can it persist?

[Arix]

Both can be answered just by looking at the text for persist. When it goes to your graveyard, if it has no -1/-1 counters on it, it persists. That's really all there is to it.