Can I carry fried rice and dried chicken preparation?

For hand baggage:

maximum size of hand baggage not exceeding 7.0 kg and of dimension - length 55cm + width 35cm + height 25cm respectively

Your poster has two dimensions that both exceed all of the length, width and height allowed so even rolled up would not comply.

If you have very little other hand-luggage, the flight is not too busy and you have an amenable check-in clerk you might be allowed to carry it with you on board but this cannot be guaranteed.

For the food I take it you also mean in the cabin (on the basis that if checked-in it is not you that carries items on board) and there the IndiGo ruling is:

Items determined by us to be of excessive weight or size, or of an offensive nature, will not be permitted on board.

and

IndiGo reserves the right to refuse to carry any large pieces which we feel may present a safety risk.

So you might want to contact the airline in advance and request official written confirmation so, if allowed, you have something to counter anyone who is inclined to disallow you.

The indications from the unofficial site are that smelly or oily foods may be deemed offensive in nature:

Indigo allows only those food items inside cabin which are non-oily and non-smelly in nature.

When I cook fried rice it is smelly (though in a way I like) and oily in nature (I am not a chef).

If detected in your hand luggage prior to boarding whoever does do so has no way to be sure you have no intention to eat this on board even if it is your intention to keep it in an airtight container throughout your journey.

Yes you can carry dried food in your hand luggage. Best way to carry it within a leakage proof container inside a re-sealable plastic bag for air travel.

Poster will also be allowed but i am not sure if it'll be allowed to carry on security checkin.

Please refer permitted items by Indigo.