Index option after expiry

What happens if my ITM index option is not closed by me on expiry due to it becoming illiquid? Will it be settled by the exchange at settlement price (i understand there will be additional stt charges) and the profit earned post that will be credited to me?

Yes gets cash settled at settlement price and profit / loss posted to your trading account.

What is settlement price? Is it the closing value of index on day of expiry?

Profit/Loss = Strike - Close?

Is 1 point = 1 Re ?

I searched the net thoroughly, didn’t find answer to these questions.

For currency options, the settlement price is RBI reference rate on the date of expiry. What about index?

Closing price of nifty which is the last 30 minute weighted average price on expiry day.

Profit / Loss = Close - Strike

1 point is Rs.1 x lot size x lot count in value.

Let me get this clear with an example -

Say tomorrow I buy 1 lot of NIFTY 17500 Call . On 8th of Sep, NIFTY closes at 17750. So my profit will be -
250x50 - Premium paid

Is this correct?

Yes correct.