A Negate played before its target is a Prevent. A card that cannot be Prevented (including cannot be Negated) will function even if a Prevent/Negate is already in play. It can, however, be Interrupted/Negated after it activates.
A Negate played after its target is an Interrupt and Prevent. A card that cannot be Interrupted/Negated will function even if a Negate is played after. However, it can be Prevented/Negated before it activates.
So in your examples with CBI abilities, the answer is no. CBI abilities need to be Prevented/Negated before they activate, not after.
In your second scenario with the Interrupt and Band, once the Band finishes the EE re-activates. "All Heroes in battle" now includes the three you Banded in, so they would be discarded too. However, those Heroes' abilities activate during the Interrupt. If any of their abilities (or cascade effects such as "play next" followed by a battle-winning enhancement) remove the EE or EC from battle, the EE does not reactivate. Additionally, if some aspect of those Heroes grants protection from the EE, that protection would apply before the EE re-activates.
Example: One of the Banded Heroes has the Shields GE equipped. Shields protects its bearer from EE's, so when the EE re-activates, the Hero holding Shields would not be discarded (the rest would, so in this scenario the best move would be to only Band in the Hero with Shields.
