It seems like these are rhetorical questions rather then questions with a "right or wrong" answer.
People's morality and integrity vary, and so does situation.
Being a true animal lover is subjective to ones views, and not someones judged questions/answers.
As far as the questions go, I'll give you my own answers.
1. I would feel sad at the sight, and I would call the humane society/animal control to deal with it. A person should never approach a scared/injured/unfamiliar animal because they could seriously injure you.
1. I would certainly try to move the cat from the street, and if it wasn't freaking out I would take it to the vets. There is no humane society here that would come out to the aid of a dieing cat.
2. I would help to dog regardless, or atleast alert the dogs owners as quickly as possible to cause the dog less harm and have them come get the dog out in a prompt mannor.
3. I wouldn't pick up the seagull, chances are I would end up chasing it around the beach. I suppose the best solution would be to alert the life guard.
4. I would RISK my life for my own dog. He is like my family. I wouldn't sacrifice my life for nearly anything, meaning if I knew for a fact that by saving the animal I was going to die, I wouldn't do it. But if there was a chance that I would make it, I would certainly attempt it for my pup Remington.
I don't know if all of my answers make sense to anyone else, but hey I gave it a whirl.