Let's just say, there is public transport, but it's not something you want to take. There is no metro. There are buses and commuter trains, but in both cases, they are so crowded and decrepit that anyone who can afford to avoid them does so. You don't have to get a car and driver, but prepare to take a lot of taxis. That is what everyone (including Indians) does.

Quite safe walking around in the daytime. And "big city" rules apply at night. In most cases you will want/need a taxi anyway, because the city is quite spread out.

First of all, just accept that you are going to spend a little time sick--stomach-wise--no matter what, if it is your first visit to India. Come prepared with things like Immodium and *possibly* Cipro if you are feeling very nervous about it (the latter will usually be superfluous, but will really come in handy if you get a severe bacterial bug). Do insist on bottled water, which is available absolutely everywhere. If you are staying in a reputable hotel, you can drink their water and ice--not to worry. The usual warning is to stay away from raw foods, but I never do that, nor do I try to be cautious about what I eat, because the food is fantastic and I want to eat everything. I have spent so many years traveling in developing countries that I no longer get sick. You WILL get sick. Just expect it, deal with it for the 24 hours it lasts, and then go back to eating everything.

I mostly eat at places that friends/colleagues take me to, or places that I hear about via reviews etc. But on my first trip to India my friends and I did a lot of winging it, and I still do that sometimes too, when I'm there on vacation. Anything with a lot of people in it is going to be fine, just like anywhere else in the world. There are a LOT of restaurants in Bombay and all over India--Indians like to eat out!

You are correct!