@Anonymous We understand you have questions regarding the pricing of your Azure Web App.
Please note that the pricing you shared in your screen shot appears to be of a "shared" tier or D1 tier web app. This shared tier web app does have a small monthly cost associated with it. From the cost column, this would seem to be roughly in the range for a shared/D1 tier web app. For more information on pricing, please see this page here. Be sure to select your datacenter region, and currency to receive an accurate estimate.
If you still feel that this is incorrect, please reply back with a screenshot of your Web App in the Azure portal under the scaling blade so we can clearly see that it is running at the F1/free tier.
My best guess is that you did not click "save" when changing the tier of your web app.
Note: We are not allowed to provide pricing guidance on the forums. If you wish to receive official price estimates, please open a free billing support ticket here.
Let us know if you have any questions or concerns.