If she's throwing up that much, you need to watch her closely. Make sure she gets plenty of water so she won't be dehydrated, withhold food, and when you do feed her, it should be something bland like plain rice, or rice and boiled chicken. If she's not better by tomorrow, I'd take her to the vet immediately.

Sometimes, ice cubes can help with hydration. Two of mine will eat them, two won't, so you just have to test to see if it will work.

Please be nice to that cat (as I know you will be). It obviously is lonely and is looking for comfort or shelter. I know I would be distressed if any of my neighbors wanted to "shoot" my cats.

Logan