I'm not sure which mobile suit the girl is supposed to be portraying. She's wearing Zeta Gundam's head fin but her uniform looks Zeonic to me.

Meh, the whole design of the "Unicorn" gundam is screwed up, why cant it look like an unicorn (a single freaking horn!) if its going to be called "unicorn" misleading ftw

When Unicorn Gundam isn't in destroy mode, it has the single horn you're looking for. post #219348 is good example of this.

The weapon was about to be handed off to the Neo-Zeon forces. It was intended to go to them. Then of course, the main character gets his hands on it.