For your main question, you can indeed interrupt an interrupt ability.
Errata, page 4 wrote:
Q: Is it possible to interrupt an interrupt?
A: An interrupt can be used whenever its rules are applicable.
For example, the Team Leader declares he is moving away
from a rogue clone, and the overseer interrupts the move with
a Surprise Attack. The Team Leader can respond to Surprise
Attack by using his Keep Your Head Down kit card to raise his
For the second question, I seem to remember there was a reason why my group ruled that the increased Max Adrenaline did count towards the preventing the clones from receiving a red die. I believe the wording on the card actually says to increase the maximum amount, but if the card text just allows an extra counter above the limit, then I would think you are correct here. I can't check at the moment (game is in a store locker), but I think I need to look at this again.
For the Dashboard spawn abilities, I once again refer you to the Errata:
Errata, page 3 wrote:
Q: How does the ready cost of the overseer dashboard
ability Clone Reinforcements work with rules that reduce
the cost of abilities that spawn clones?
A: The “2” in the cost circle for the Clone Reinforcements
ability is the base cost. The text of the ability allows the
overseer to spend more adrenaline tokens when paying that
cost to add more clones to the number spawned. All the
tokens placed in its well when you activate it are “the cost.”
This means that spawning three clones costs six adrenaline
normally but costs only five adrenaline if the cost of spawning
clones is –1.