If you want to tweak these settings, you should first change them at the account level, and then customize as needed on a per-property basis.
To edit your account-level Tenant Alert settings, go to My Account -> Settings -> Alerts.
To customize for a particular property's tenants, click on "Customize" when adding or editing rent details for the property:
To disable an alert, simply uncheck the delivery method checkboxes for the alert.
Finally, be aware that this simply sets defaults that tenants will be able to override for themselves if they'd like.