I won't pretend to know what all that means but WooHoo RT!
Generation Break = Meeting certain conditions that progress the plot of the mission and cause enemy/allied reinforcements to arrive.
Over Impact = Optional Generation Break after all the main ones are completed that turns all your allies into enemies, allowing you to capture some of them under certain conditions (to capture the Strike, I had to destroy the warship it was assigned to).
Secrets = Secret bosses that spawn if you meet the Generation Break conditions under even more strict conditions.
Example: If the Gen Break is "defeat the Strike in 5 turns", the Secret condition for that Break will probably be "defeat the Strike in 3 turns", or if it's just "defeat the Strike" it could be "defeat the Strike using a beam saber" or "defeat the Strike with X character".
As for the names~
AEU Hellion:

Gaza-C:

which can transform to/from

Strike Gundam:

which can equip optional equipment (and change them mid-mission by returning to the warship) to become
Aile Strike:

Sword Strike:

Launcher Strike:
