What happens if I don't exercise my options?

If you dont exercice ITM( In the money) options then exchange will buy the option with excee STT of 0.125% on the turnover(Strike price+premium*lot size) not on the premium.

All the ATM(at the money) and OTM(out of the money) options premium will become zero on expiry. 

If you hold a bunch of options and it is in the money at expiration date… you don’t explicitly sell that option nor do you exercise it and therefore it remains in your portfolio past the expiration date…

Will brokers typically will then return the in-the-money value of that option to you in the form of cash, or do you just completely lose those in-the-money value due to neglecting to sell/exercise the option within the expiration date

After the closing of trading on expiry day, exchanges settles all the ITM options automatically. So your options will be cash settled and will be credited to your trading account by the broker.