Hi @Thisisthedawningoftheageofaquarius
I worked in India for three years, working with public and private sector stakeholders in an organisation with a mix of Indians and foreigners.
On weather, bear in mind that in October the pollution will be bad in North India. If you’re going to Delhi, Haryana, Punjab, Rajasthan, I’d advise you to get a pollution mask - Cambridge Masks are good if expensive. And plan your outfits for the potential that you might want to wear a mask with them.
I agree with @Sweetwindinmyhead - in the cities, India isn’t as conservative as you think in terms of dress. You can pretty much dress as you’d dress at work here. I think @elaeocarpus advice is sound though, to err on the side of conservative until you get a feel for the place, to avoid being uncomfortable.
Bluntly, if you’re white, there will to an extent be an expectation that you’ll dress ‘western’. If you have south Asian heritage - in your name or appearance - there is more of an expectation that you’ll dress more modestly. This was the experience of my British colleagues with south Asian heritage as well as of my Indian colleagues.
Chennai will likely be pretty hot and humid. Cotton is your friend!
North India will likely be quite cool and pleasant. Again, I would recommend cotton though, just to stay comfortable in case it does get warm.
Open toe shoes are totally fine, in my opinion. Bear in mind, when considering shoes, that pavements and roads are often pot holed, bumping, don’t have great tiling - I stopped wearing heels (except for meetings where power dressing was needed!) pretty quickly.
TLDR: don’t panic, erring on the side of modesty is safest but generally not necessary, cotton is your friend.