I went in 2015 for work including Delhi, Bengaluru, Delhi (along with the Taj Mahal) and Pune over a 10 day period. As people have mentioned - your visit timing will be intensely hot, humid, and monsoonal conditions (wet) might be the case. Like visiting WDW in the summer
If you aren’t a city dweller, be prepared for very crowded and dense conditions - in traffic especially - I would not recommend driving and where possible to rely on private transportation or tours where your budget allows. I was fortunate to have a colleague on my travel from India and it was incredibly helpful to have their insight - perhaps your sister will be acclimated by this point and she may have some friends that would be willing to help with the touring.
While for the most part, I felt safe in most areas - I never ventured out too far on my own and the people were very welcoming and friendly. As with many major urban environments, soliciting was an issue - especially by children and even while waiting for traffic jams to clear - they would walk up to our vehicle. Always be situationally aware in your surroundings - which is just a good standard practice traveling anywhere.
We took a few internal flights from city to city on our trip and the equivalent of waiting areas, security screening, and flight schedules were challenging at times. Bring your patience pants. In leaving Delhi back to Paris, there was a security Issue in the Airport with a lock down - which took several hours to clear. Security screenings at the major western hotels are common - including checking vehicles with a mirror underneath the car before being granted access to the grounds.
In Delhi (Embassy area), I had several families approach me to be in their family tourist pictures - this also happened in the Taj Mahal area a few times - it was sweet but when first approached - it was a little strange. We took a private car and tour to the Taj Mahal - it’s a pretty long drive (3+ hours) and we stopped at the equivalent of a large truck stop / quick service for lunch. I felt like the world was starring at us but everyone was smiling. Being at the Taj Mahal was surreal - so definitely a must do.
I thoroughly enjoyed our trip, everyone was welcoming and friendly - the food was amazing - and typical cautions in drinking tap water should be observed as well. Be sure to take anything offered or hand anything to someone with both hands and never only the left.
Because the trip was mostly work oriented, I didn’t have a lot of time to get around a lot - leaving it open for another trip!