Yes you can use excel to create a schedule. As for your question about having it select from 29 people and randomly generate days on, and days off with a max of 8 or 9 days off? we might even be able to get excel to do that but I think simply creating a schedule your self where you can adjust it to people's personal request or needs would be better.
Since this is a 24 hour project and a 7 day a week program.
I have created a very simple schedule for you to look at.
Things you did not specify in your question.
How long is a shift.? I would be assuming 8 hours due to the 3 shifts and 5 day work week
When is the shift change.? Normally day shift around 6am, 2pm, 10PM
so I hope this helps you