Yes, Tata Indigo eCS LS (TDI) BS III comes equipped with Central Locking as a standard feature. To know more about its features, kindly visit the below link: -
We will suggest you to go for Amaron
AAM-FL-555112054 battery or Exide
FEM0-DIN55, while the Amaron battery will cost you around Rs. 6200 without old battery and Rs. 5000 with old battery, the Exide battery will cost you Rs. 5500 with old battery and Rs. 6300 without old battery.
The engine check warning comes, when something went wrong with your car like, it get heated or something went wrong with the electrical. Whenever it comes, check what is wrong with the car, if you don't find any visit the workshop.