Okay. For Engineer, how about Nailgun (weaker but can repair buildings from a distance and has faster reload), and for the melee, a Drill. Allows you to heal/build/upgrade buildings twice as fast but cannot hurt enemies.
For the secondary, I'm not sure.
a building mover
I could make sweet, sweet love to you right now.
So basically, it'll be like a PDA. Since the buildings look collapsable, they'll quickly collapse into a box shaped object for the Engie to carry. He can have multiple buildings ready for movement at the same time, but can only carry one. When the building is dropped, it'll pop open again and resume it's duty. It'll also have the same HP, level and upgradeprogress when moved, so don't think it's like building a new building.
Bad thing. I wouldn't recommend using the Building Collapser unless you are near the building. I will make it so enemy Engie's can pick up your collapsed buildings if you just leave them there. If an Engie carrying a building is killed, he drops it, but it stays collapsed since he didn't allow it to uncollapse yet. Meaning it's up for grabs.
Semi-good thing. Ally Engie's can also pick up your buildings. However, it will belong to them if they put it back up so they will get the points from it.