Where is the goose you saw? Carolina waterfowl rescue takes in and rehabilitates waterfowl but if it’s too far of a distance they rely on volunteers to capture and transport injured birds to them.
This case here is more of an issue regarding an injury to the joint and not a vitamin deficiency. B vitamins can boost the immune system and help the liver to cleanse and heal itself so regardless even if there isn’t a deficiency B vitamins can do a lot of good.
The dark green droppings are cecal poos, it’s normal.
If all of the droppings were a bright green color that would indicate an issue, possibly organ or digestive issue.
You can try giving him/her some flock raiser or all flock type food to get his weight up.
As for the joint, I’m in...