Uh, Wonder Woman's stamina and HF are both godlike, that's kinda her thing too. I don't think Thor's healing is better than hers, I'd guess they're fairly close.
Even if his durability and HF are significantly higher than Diana's, it's not going to matter a whole lot if he can't reliably hit Diana as often as he would like to, when in comparison, she'll be able to tag him often and not be hit nearly as much.
Not without magical aid, I'd imagine, but who knows. Her connection with the earth might enable to do this, though I've not heard of any case in which this happens. In any case, neither can Thor on his own.
Thor can if he use odinforce (but magics a part of him like with Billy so they can use it on themselve right? unless OP says their cut of from there magic source for the fight)
I think she could when in contact with Gaia. She's recovered from being stabbed often enough, and they said the only reason her eyes didn't heal after Medusa was because of who made it, and that nothing would restore them (eventually they were even replaced, not restored).
At the least, wounds to her flesh heal up quite fast.
His own Asgardian phisiology, unaugmented by Mjolnir or the OF, wouldn't enable him to regenerate lost limbs or organs, but it would allow him to survive from even the most dire of injuries. Billy's regeneration is whole nother animal.
She's made from what? Dirt or clay or whatever so I if she lost a limb she would need to be turned back into clay like in the past and she should be back to normal once remade. It should be pointed out that she's just a demi-god like Hercules. Thor parents are an Elder Goddess and a Skyfather since they're all being compared. Not that it matters much.
Clay of Themyscira animated by Athena's blessing, which also gives her a strong connection to Gaia which gives her a healing factor that's boosted when in contact with Earth. Diana's immortal to be sure.
I suppose if one wants to be technical, she's more a divine golem who serves as a godly champion.