If Surge Engine loses defender in some way other than its first ability, its second ability may still be activated. Likewise, if it becomes blue in some way other than its second ability, its last ability may still be activated. Note that an effect that allows a creature to "attack as though it didn't have defender" doesn't actually cause it to lose defender.

Surge Engine's last ability can be activated only once per game, not once per turn.

If a Surge Engine whose last ability has been activated leaves the battlefield and comes back, it's a new object on the battlefield and its last ability can be activated again (once it's blue, of course).