Some unanswered questions.

[Kein]

Why was Daniel able to simply piece an Orb back together with some adhesive (twice), when evidently Alexander could never do so himself with his own broken Orb?

Indeed. I wondered about this too... And what became of that pieced-together orb? You put it in the stand, go sabotage the machine, come back, the orb is gone. Did the Shadow absorb it? Some monster take it?

I would also say Alexander isn't just a human. The portal leads to "another world" and he wants to "return home" there.

If you destroy the machine first and then set up the orb... well, you will see ;P