What about the other shards?

[Enkidoh]

Most of the other shards no longer exist as they were all destroyed when they were Rejoined (seven in fact, one for each Calamity that have occurred on the Source), plus one has become completely lost to a Flood (becoming the Void, and which we actually have already travelled to - it's the World of Darkness). Really, not including the First and the aforementioned one that was lost to the Flood of Darkness (the Thirteenth) there's only four Shards left that are not yet Rejoined. As for how their cultures and history are like, well, given Norvrandt and it's cities clearly shows similarities to Eorzea on the Source, while wildly diverging in other ways, they wouldn't be too different to what we've already seen.

As for whether we will be able to visit them too, it's hard to say, although I'm liable at this time to say no, on account of the means we were able to travel to the First was an exceptional circumstance that has been forever disabled (due to the events of the Twinning dungeon), so unless another means of overcoming that troublesome 'only aether/souls can pass between the Source and the Shards unless you have a dimension-hopping crystal tower powered by part of Omega and Alexander' limitation becomes apparent, I'm not expecting to visit the other Shards any time soon.