The other answers are good but don't seem to directly address one of your questions:
Wasn't protecting it the reason why they revived superman?
No, they revived Superman to defeat
because they were not strong enough (they all tried and failed, both individually and together). Even without the motherboxes in the picture, he could still defeat them in combat, and thus could potentially end all life on Earth, it would just take a long time.
Originally, they were protecting the motherbox (which they didn't fully understand1) to prevent it from being combined with the others, so that the Big Bad Thing didn't happen.
Once they had the idea to use it to revive Superman, the priority was to protect it/hold onto it long enough to use it for that, the hope being that a revived Superman would be strong enough to defeat the enemy.
With Superman revived, as others have already explained, their immediate concern was to make sure he wasn't a crazy monster, like Doomsday was. Plus the notion of resurrecting someone from the dead (or stasis, if you prefer that term) is a pretty insane thing; you'd want to stick around and check out the result for yourself. They also probably weren't expecting the motherbox to fly off like that.
One exception to that is Victor Stone; as Victor, aka Cyborg, was essentially merged by his father with the motherbox in order to save his life, Victor/Cyborg shares its 'DNA'... for lack of a better term. Given enough time, he could theoretically understand it pretty well. But he is only recently Cyborgified in the movie, so he's still coming to terms with his capabilities.