To build nukes, you need the techs Rocketry and Fission, they come very late in the game so focus on your economy. You will also need access to Uranium, and somebody to build the Manhattan Project (it comes with Fission, you can do it yourself, but itll allow everybody to build nukes if they have the tech and Uranium). The best way to grow cities fast is settling them near good sources of food (cereals, livestock, seafood), but the biggest limitation they have early game is usually happiness, which you can solve by spreading religions and building temples, aquiring luxury resources (precious metals, gems, spices), adopting Representation/Hereditary Rule etc.
Religion gives happiness and culture, and certain bonuses with the right civics, it also boosts diplomatic relations with leaders with the same religion, and damages them with leaders that adopted a different one. Oh and you can even win if you spread your religion everywhere, with the help of the Apostolic Palace. Culture output helps you claim more land around your cities, even make nearby foreign cities join your empire peacefully, it also adds a defensive bonus to cities that increases with cultural level, and is the only way to achieve a cultural victory.
About mines/farms, people here say that Slavery is broken, and makes food much more valuable than hammers, so maybe its best to focus on working farms.
