Q. If a product isn't assigned a price, will it publish?
Yes, it will publish in the system 
You can set the item to hidden until a price is applied, so it won’t be visible on the customer’s end.
There is a warning that appears when you try to save an item at $0
Sync will override this to the sysnet price overnight

Q. Can you duplicate a modifier?
This is not possible
Modifier options can be reused and only need to be created once
When copying a category from the master site to a venue, it will copy across the modifier group attached (will show you in the next session)

Q. Price adjustment – how does it work if special pricing is set in Pub+ and Sysnet? Which price overwrites which?
pub+ pricing will take priority.
Need to validate the experience if the pricing on me&u/H&L is lower than Eagle Eye

Q. Can you apply a price adjustment to modifiers? (e.g., Schnitzel & Topper)
There’s no way to apply a price adjustments to modifiers

Q. Can 2 price adjustments be applied to the same special? eg Kids Meal & Drink - discount $1.25 from the meal & $1.25 from the drink
We can apply 2 price adjustments as long as they are not on the same item. For example, 1 price adjustment for the Kids Chicken Nuggets and 1 price adjustment for the drink. However, if we are applying 2 price adjustments to the same item (e.g., the Chicken Nuggets), make sure the timing of each price adjustment doesn’t overlap, otherwise one adjustment may overwrite the other.
In your scenario, it would be 1 price adjustment and both the food item and the drink item would be discounted $1.25 each.

Q. Can we set up a time block across multiple venues for an item created in the master site? This would eliminate the need to activate/deactivate Footy Jugs on a Thursday & Monday.
You can copy across Daily Specials.
I will investigate this use case and report back findings on Wednesday.