Moving to India

My partner and I are moving to India as a career move. I'm not on a mega fancy expat package but it's a good salary in mainland china (we are Korean and Taiwanese). We are thinking Mumbai. It would be to set up a new office. I am looking for some practical advice:

• We are a lesbian couple, will we need to be closeted in public? No holding hands, kissing etc...?
• Do people use apps to find apartments? How would one find an apartment without getting scammed?
• What is the vet situation like? We have two cats who would be moving with us
• What is transportation like? Should we rent a car/driver? Or is Uber enough to get around. (We don't need/have a car in Shanghai)
• How much Hindi do I need?
• Where can we get dependable housekeeping?
• Online, it's been hard to get a good gauge on cost of living. How much does a decent upper middle class lifestyle cost? Gym memberships, meals out 3 to 4 times a week, taxis everyday, health insurance, tennis etc...

There's so many unknowns - anybody who's made the move to Mumbai with tips on how to make it as smooth as possible?

Thank you for any advice in advance. Really excited as I think India is the next/already big thing in world economic history. And we love Bollywood.