Using the EWS Managed API you can create appointments within your Web Form. Here is a link to a "How to" topic for creating appointments that has come C# code you can work with:
How to: Create appointments and meetings by using EWS in Exchange 2013
In order to save it to a public folder you will need to get the FolderId and use that when you do the Appointment.Save()
method. There is some sample code to work with in this topic:
How to: Work with folders by using EWS in Exchange
I hope this helps.