The "Khans" ability triggers at the beginning of both your precombat main phase and your postcombat main phase. Unused mana is lost at the end of each step and phase.

For the "Dragons" ability, you decide whether the creature with flying will fight the target creature you don't control as the ability resolves.

Each Siege will have one of the two listed abilities, depending on your choice as it enters the battlefield.

The words "Khans" and "Dragons" are anchor words, connecting your choice to the appropriate ability. Anchor words are a new rules concept. "[Anchor word] — [Ability]" means "As long as you chose [anchor word] as this permanent entered the battlefield, this permanent has [ability]." Notably, the anchor word "Dragons" has no connection to the creature type Dragon.

Each of the last two abilities is linked to the first ability. They each refer only to the choice made as a result of the first ability. If a permanent enters the battlefield as a copy of one of the Sieges, its controller will make a new choice for that Siege. Which ability the copy has won't depend on the choice made for the original permanent.