Will Parachute Backup ever delete anything from iCloud or from my backup?

Never from iCloud. Parachute Backup only reads from iCloud and never changes or deletes anything there.

By default, your backup only grows: new and changed items are copied, and nothing is removed. If you turn on Remove Deleted Items (Mirroring), items you delete in iCloud are moved to a folder named Deleted at your destination instead. Under Keep Items you choose how long they stay there: forever, 90 days (the default), 30 days, or until the next backup. Until then, you can move them back at any time.