yes only once per person do
it was not destroyed because in order for the horcrux to be destroyed, harry would have to die. When the basilisk's fang pierced through his arm, he did not die because of Dumbledore's phoenix which is said to have tears that heal wounds. So the phoenix's tears healed Harry, so he did not die, so the Horcrux was not destroyed.
Phoenix tears can heal any wound, cut, scrape, or bruise.
The Phoenix's healing tears will only work on injuries. Dumbledore was hit with the killing curse which stopped his heart but left no wound.
NO
It is able to heal with its tears. Fawkes also goes through repeated life cycles. He burns to ash, comes back out of it as a hatching, and begins growing all over again. During the duel at the ministry between Dumbledore and Voldemort, he swallowed the killing curse that was directed at Dumbledore. He burst into flames, but was reborn. A phoenix's feathers also have magical properties which make them suitable for wand cores.
If you're talking abound heart wounds then yes, but only if you want because we all know that phoenixes are a myth, so you have to use you're imagination and your will power because most of our pains whether be in our body or soul comes from our mind.
Anti-venom
YES IT CAN
Use a Phoenix Down on them, or a Life spell.
When you exersize, your muscles get midroscopic tears in them. When these tears heal, your muscles get bigger. This is how you get stronger. The more you exersize, the stronger you Muscular system gets.
if you mean how did harry heal his hands in the book thhen he used essence of dittany if you are talking about the game idk.
one of them is that they can heal wounds with their tears, I'm not sure if this goes for any illness or just wounds. and, because they die and be reborn they obviously live forever. and i think they might be immortal? I'm not sure about that one.