I have a question about stealing items. For example, the Spoils card Court Collar allows me to steal a scepter.
I assume that means my opponent must have a scepter, else I cannot "steal" one.
Correct. The same applies for gaining an item; if there are none in the supply you gain nothing.
More importantly - if the scepter is flipped over (inactive), when I steal it, does it stay flipped, or do I flip it back to the front so that I could use it later that Night?
No, if you steal an inactive item it remains inactive.
Also, if both players have a leader in the district, who places their marker first? The player with Supremacy? or the player who won the district, and then if tied the player with Supremacy?
That's actually a pretty good question. I can see how there's a bit of wiggle room since the rules for Seizures have it broken down into 2 steps.
So an example:
Player B has supremacy, but Player A wins the District. Player A places 1 or 2 markers depending on the night card in play. Both players have a Leader in the District. Does Player A place the first marker (having won the District) or does Player B (having supremacy)?
Personally, we've played that the player who won the district continues to place their markers first. I'm kind of curious how much of a swing there could be in a game if it follows supremacy instead.