Will I be charged if I host my application on Azure App Service more than 60 min even if my app does not do any processing?
The answer is NO.
Under App Service -> App Service Plan -> Quotas you can see a detailed breakdown of usage such as an example below for a website I created hours ago but showing only 1.11 minutes of usage:
I got the answer from AjayKumar-MSFT's answer from this post at a Microsoft forum, then proceeded to test it myself.