I can’t keep him/her. Are there any places in NYC specifically that I can take this baby too immediately?

This poor baby appeared at my bird feeder, and I want to make sure that whatever she is suffering from isn't contagious to our other visitors. This is my first time seeing her. She appears to have this mass on her side as well as her beak. She seems to be fully active and I am unable to catch her. Please advise! Located in Western Washington. Spoiler due to injury pictures!

Found a tiny baby western meadow vole in the road, need to take it a wild life place for care none of local ones are helping, the one in pefferview said they will take him but I dont have a way of getting there lmk if anyone can take him or help currently in peterborough

We found this baby bunny in our yard yesterday that hasn’t opened its eyes yet. It looks like it cannot use the back legs since it is just crawling and dragging the back legs. We decided to put it in a box after it was sitting at the same spot for the whole day. We have fed little bit of kitten milk with a feeding bottle.
This has never happened to us and we don’t know anything about rabbits so if anyone can help us answer some questions I would appreciate it!
1. How old does this guy appear to be? I am guessing a couple days old but wanted to make sure
2. Should I keep feeding him kitten milk and take care of it? We are open to permanently taking care if needed
3. Any other advice?
We live near Dallas, TX
Thank you so much!

We tried to catch twice with no luck because it can fly, my yard isn’t fenced, and there is a pond access in my yard. We have two ponds in the neighborhood, and right now it’s staying close to my yard during the day then flies toward the back pond for roosting every night.

Should I keep trying to catch if I get additional help (which always proves to be hard to find)? Or can this goose eventually heal to be strong enough to survive on its own?

I have spoken to a licensed rehabber and would bring it in to the wildlife hospital if I do catch. There is no one that will come out to catch it, so it would be up to me to catch & transport.

I’m conflicted because I don’t want it euthanized if it’s capable of surviving after the initial healing. But I also don’t want it to suffer if surviving means severe limitations and pain for the rest of its life. The ankle has been broken for 8 days at this point.