Clockwork Princess question

I believe the third condition was getting Jem aka "Brother Zachariah" to come talk to Will and Tessa.

Yes what Jasmine say. The third condition was to let Jem have one final talk with Tessa and Will to break his relation ties and say goodbye (I cried throughout this whole part).

Same with Angie, I thought the third condition was to let Sophie Ascend. And didn't Charlotte say she wanted to train Will to run the Institute?

I think that maybe the third condition was to ascend Sophie.
And about the institute, weren't Gideon and Sophie running it? or maybe Cecily and Gabriel?