When designing a new Sovereign there are some hard choices to make. Which magic to start with impacts the Sovereign initially; e.g. "Do you want an early Tutelage bonus of +25% Xp or not?". And it also affects the starting city/cities somewhat (even though this diminish over time as you get more/better city-buffs), e.g. "Do you want the Enchanted Hammers (+1 material) or Inspiration bonus (+1 research) from start?".  Therefore I concluded that your first Champion also has an impact to your starting strategy (adding options to buffing Sovereign and cities). This is especially noticed in games where you have very few quests and thereby wait a long time for the second and third Champion (i.e. my current game).

This is obvious of course, but when I design my Sov, I want to know what Magic schools can be complemeted by the Champions later. Therefore I reloaded the only scenario a few times and discovered the first Kingdom champions were selected from 6 people (and I assume these are identical to the ones I was offered in a non-scenario-game using the same map).

Bannon Heighsley - Water, Command, Soul Spark (Amarian Blood, +1 different stats/shard)
Inslow – Earth 1, Rescue (Altar; Rush and +10% Xp)
Hannis – Earth 1, Guard strike (Ironeer; +1 Hp, +50% magic cost and 30 spellresist)
Othollo – Fire 1, Revenge (Altar; Rush and +10% Xp)
Ralle Stormborn – Air 1, Channel Lightning (Mancer/+1 move and +1 Acc/lvl)
Iriel – Life 2 (Amarian Blood, +1 different stats/shard)

1) Are the available Champions always the same, or do they differ from map to map? (assuming you choose the same Kingdom or Empire side)

2) What are the available second and third champions for Kingdom? (tried searching but found nothing) 

3) Are you always only allowed to choose class for your first champion, or is this scripted in the map/scenario?