US patents are generally not valid in India. As I understand it, you have to patent something in every country where you want protection. In practice, you choose how many countries you need, in order to protect a reasonable market. Sometimes you can guess wrong about this, of course.
It does, but as I understand it, you still choose where you want to apply for a patent (and consequently, how many fees you have to pay).
I have a number of patents. For my earliest ones, the lawyer suggested filing in the US, and in any country where a competitor was located. Later we started filing in US, EU, and in some cases Japan. Today, China is on the list, but not India.
Same as for EU countries where software patents are not valid. You can make a product that violates US software patents, but not sell that product in the US market. Depending on your business model that may be acceptable or not.