begged Castillo to go and attend to a man who had been wounded, as well as to others that were sick and among whom, they said, was one on the point of death.
This part reminds me of the Bible. Particularly the gospel of Mark when Jairus' begged Jesus to cure his sick daughter.
because all had gone to their abodes after gathering tunas
They could also be gone due to traveling for food and resources.
recommended them to God, at that very moment the Indians said that all the pain was gone.
Due to Castillo's belief in God he more than likely said the pain went away, even if it did not.
Avavares
Another tribe Cabeza de Vaca met on his travels.
Mariames
A tribe that Cabeza de Vaca lived among