The outbound IP addresses will change, however the DNS record will remain the same, its usually recommended to connect to an Azure App Service using its CNAME.
Differnet Azure plans, have different functionality, such as different backup requirements, autoscale rules the ability to use cutom domains, moving your app service between tiers either enables or disables the functionality, ie 50 daily backups go down to 10.
Other than the limitations above, downgrading an App Service will cause an outage, so needs to be done within a maintenance window. Before resizing, its worth stopping the app and restarting the app to make sure it comes up after a cold start as well, before proceeding with the resize.