There was no invasion of India by Alexander. He barely crossed modern day Pakistan and parts of Punjab before heading back. Magadha was still untouched and so where all southern kingdoms. India is not Delhi and adjacent areas of Delhi which speak Hindi.
As for rest of your comment, I don’t know enough to comment on it. On cursory reading it seems you are right and thank you for this information.
>India is not Delhi and adjacent areas of Delhi which speak Hindi.
Don't have to be the whole of India. Just to be part of it. That's like saying someone who went to a tour of New England didn't visited the United States, because "New England is not the US".
As for rest of your comment, I don’t know enough to comment on it. On cursory reading it seems you are right and thank you for this information.