Garlemald's War of Succession starts sometime between the end of 1.0 and the start of 2.0. We don't have a hard confirmation on exactly when it started or exactly when it ended. We do know the Eorzeans have word that it ended by around the 2.3 -2.4 time period, but given how little intelligence they have from the Garlean Homeland, that doesn't mean much. It is very likely we well be getting a thorough run down of the War of Succession in the coming patches/expansion.

The War of Succession was what Giaus decided he wasn't going to have anything to do with and is why he and the entire XIVth Legion are considered traitors back in Garlemald. If he had gone back to take part in the War of Succession, then Garlemald and the Ultima Weapon probably wouldn't have been in 2.0 to begin with. On the other hand, that's what leads to Gaius finding out about what the Ascians true plans are, which from the looks of things, no one in Garlemald knew about.

Edit: I really need to learn not type up stuff ASAP if I think Anonymoose will post on it...