There was another thread that I responded to with my thoughts on the matter regarding Eldar Rangers. The thread sorta got detailed shortly after as they ended up talking about the strategem Phantasm, but you can ignore that bit
https://www.dakkadakka.com/dakkaforum/posts/list/743814.page#9682927
EDIT: Just woke up and clearly forgot to read things. Anyway to answer your questions:
1. Yes they do as it happens outside of the deployment 'phase'
2. They are placed at the beginning of the first battle round so I think in order to determine proper turn order and allow the game to begin, they are placed after the seize roll
3. Roll off would be the go-to answer in that case,
IMO