Visa - Indian passport holders can apply for an e-visa if they have a valid US or Schengen visa, which is what we used. The process is straightforward & hardly takes half a day. You can apply here. It costs around USD 85-100 depending on the source of the application.
Without US or Schengen visa, you need to apply via VFS & the process can take up to 10 days.
Getting around -
Taxi - Uber works but is quite unpredictable. Drivers usually prefer longer rides & cancel when you tell them nearby locations, which kind of kills the point. Works best for 10km+ rides & to & from airport
Public transport - Istanbul has a good public transport network of trams, buses & metros. You can find all details & fares here. It's best to get the card & keep topping up as required. Top-ups are available on most stops via self-serve machines or kiosks.
Flight - We took Gulf Air flight from Kochin with a short layover in Bahrain. Highly recommend the airline. New aircraft, good service, very friendly crew.