It's case old saying lost it's relevance.
This is absolutely correct in developing countries which only has one main railway station or bus stand for the whole city or town. These establishments targeted one time customer who will never return in a year. Including metro is not valid or violation of the actual circumstance this saying originated. Including Mtro and even if still counting walkable distance of 100 m from the station almost covers the whole city. Doing this in Paris with more strict enforcement of food safety and quality isn't really going to validate.
She spoke French and English from childhood, her family spoke those languages. I cannot accept English is her native language.
English language as a whole is not fully single language. It has influence of many languages. Only a portion of the language can be considered native that has substantial contribution from England etc. Other parts are not native or something anyone needs to feel their own.
Most languages are not purely from a region or a race except some tribal languages. I have no particular liking for the language I spoke as a child. If you go deep some influences on it are forced to suit a particular identity. Maybe not European languages. Test is whether our ancestors spoke what we consider our native language 500 years ago.
Maybe I will shift to a language I have never spoken in life.
I'm not sure I understand that point you're trying to make. As someone who only speaks English, if English isn't a "single language" or "considered native", then what's my "native language"? My understanding of the term is that "native language" is descriptor of a speaker rather than a categorization of a language itself, so the idea that a language itself can be "not native" universally doesn't make much sense to me. I understand that different parts of English have roots in different languages, but from my perspective as a modern speaker with only limited knowledge of other languages (a few years of Spanish in school and then a few semesters of Dutch in college, but I'm not even proficient at a conversational level of either at this point), the origins of the words I'm using are irrelevant to whether I can think naturally in them; the fact I can check Google to see the entomology of the words "check" and "proficient" and see that one comes from French and the other from Latin doesn't affect my ability to understand them being used in this paragraph together. I strongly suspect that anyone else who identifies as a native English speaker would similarly be able to understand both of those words equally well, so it's not very plausible to me that there's no such thing as English as a "native language".
Sanskrit is a language that goes beyond Hinduism. Almost all important Buddhist Sutras and influential works like Mulamadhyamakkarika or Jaina works like Tattvartha Sutra are in Sanskrit.
Lastly Sanskrit is also the language of many secular works like Siddhanta Shiromani, Sushruta Samhita, Kama Sutra or Abhigyanashakuntalam.
I have been reading a LOT on the topic. The date ranges usually from 1700-1200, mostly skewing towards 1700-1500. Mostly they date it based on stylistic reasons and things mentioned in them, that seem to correlate with those timeframes.
There is a good book by Romila Thapar, “Early History of India” , for the general overview of early history. You probably want her latest edition, they changed a lot over the years.
A bit more classical but thorough is a History of India by Herman Kulke and Dietmar Rothermund.
And the best one to go into detail is “The Rigveda : a guide” by Joel P Brereton & Stephanie W Jameson.