Of course we are going to need culture in that city to fight off Asoka, so do we need to look for Writing early and Library? Also when should we gift Asoka the stone
Culture in that city isn't necessery. It will get into a fight with a capital city for the floodplains just north of it, and those tiles I don't think it would be worth to fight culturally for.
The other tiles can easily be defended with just a single monument or some religion.
Catapults will ensure that city will have enough tiles in the long term.

Regarding stone, if TGW isn't built by the time you get masonry, I would want to put some chops and turns into that for failgold. Perhaps some into pyramids too, but once thats done just gift it to him asap.