Unless I'm missing something, it's unclear whether they hope to move back into the Cort once renovation is complete, or whether they expect to find a new theatre. But that's probably because they themselves don't know.
Like with all Broadway shows, nobody really knows anything definite about the timeline of the return. The 2022 date is probably just a guess/wishful thinking. It sounds plausible, but who knows at this point.
As for getting the cast back, I'm sure they hope to get everyone back, and I'm sure everyone wants to, and intends to come back. But again, only time will tell whether they actually will. Especially with the bigger stars like Armie Hammer.
Unfortunately, I have a feeling that this little bit of news might end up being the end of The Minutes, and the planned re-opening might just be a bit of a pipe-dream, like when closing shows announce a tour that never ends up happening. But I hope I'm wrong. One thing is in their favor: there will probably be plenty of empty houses once Broadway does re-open.