Candidate status means they are pretty likely to get get accredited. They have to graduate a class first though to get the accreditation. Schools that are in candidate status have to meet a lot of requirements to get that status. No school has ever not become accredited if they have reached candidate status. That doesn't mean it can't happen, but the chances are really, really low. If you want to know more, look at the ACPE website.
The written exercises are usually some broad type of prompt you have to write an essay about. Sort of like the PCAT essay. Schools usually change the prompt throughout interview season, so you won't know what it is exactly.