Should I be so worried about this cat?

by Skj
(Pune, India)

I sort of take care of a stray cat that has been living around my house for almost eight months now. It looked meek and hungry once, so I gave it milk. I read online that it's not good so switched to cat food, which it eats twice a day regularly.

It's not house broken, so when it littered around the house terrace, I stopped feeding it for a few days. But it came back asking for food, so now I feed him.

I took him for vaccination shots, gave him deworming medicine, and it's always calm with me. Never frisky or snarly.

Today while petting him, however, another cat went by and this guy suddenly jumped up with a small snarl and my finger was caught between its teeth.

I was scared silly and called up the doctor. He saw the bite and said it is clean and doesn't need and injection.

Now I'm worried:

1) Should I still get an injection?
2) Should I stop taking care of it if the smallest issue scares me so much?
3) Should I continue feeding him and try training him to do his business in the litter tray and not pet him?
4) How do people handle cats as pets?