My distribution certificate is expiring on coming week, along with all of my provisioning files.
How do I properly renew it? Should I revoke it now and request a new one? If I do that they will all my live apps be taken down?
How do I properly renew it?
Just Edit and get the updated certificate to use.
Should I revoke it now and request a new one?
No need.
If I do that they will all my live apps be taken down?
Have no effect for the live apps.
If your developer certificate is expired soon then you need to renew the developer account.
As you annual subscription is not expired, your app will be alive in the App Store.
The distribution certification is just a token for distributing your app with an expiring date.
I don't think you have to do anything until you distribute your newer version of your app. It will be automatically revoked for sure. And you may have to log in again and activate again before your next distribution.