My client had added me to his DropBox team and used my business email. I am now trying to segregate me business from his.
You need to have the team admin convert your account back to an individual account. It's very important that they don't just remove you from the team, as doing so would delete your account and they would only have seven days to restore it. They need to convert your account back to an individual account.
1.)If the admin changes my email. I am assuming that I can log into DropBox with my old email and be prompted to setup billing and retain all the files added under my original business email, is this correct?
Changing the email will do nothing. The team admin has to convert your account as described above. Only then will you get your account back and be able to resubscribe if needed.
2.)Does the Admin in Team have the ability to view all of the folders in DropBox that a team member adds, even when they aren't shared with anyone or with folders shared outside of the team?
When you joined the team, you merged your account into their Business account. At that point they were the owners of your account. While the admin can't just see the content in your account, they do have the ability to sign in as any account within their team, allowing them to see all content.
3.) If an Admin changes a team members email, the team member can view an folders the admin has setup for them to view?
Changing the email address will do nothing except change the email on the account. Whatever the account had access to previously, it will still have.