Is "paani puri or goal gappe" readily (PACKED) available in Indian Markets?

Ya u get the packet but there no brand in it u just get ready in a transperent plastic cover

There are no branded pani puri (gol gappe) available in the market. You will get the puris and other liquids/solids separately packed and you will have to do the mixing yourself. This will not give the typical taste of the street food as the mixing would be amateurish!

I do know that you can buy the puris, the filling and the paani puri water/chutney in Indian markets like Patel Brothers and India Grocers.

No, in most places you don't get packed paani puri. You get puri packed in covers and the masala to make make the paani, the most famous masala is MTR paani puri masala (method to make paani will be written be the MTR box). To make the filling you have to mash boiled aloo with chilli powder, black salt, crushed chilli's, black pepper powder and coriander masala, then add some coriander on the paani to garnish it.

Yes in hyd they will give parcel.