The WizIQ web services can certainly bring an important added value to your site and thus it's worth implementing them carefully and in a sustainable way as they can be later extended with many new functionalities.
In order to setup an account on WizIQ you must first insert your own sets of data into their registry, including teachers, students, virtual classrooms etc. so functions will have to be created for that. Since this information is likely to change in the future, it would be convenable to create an admin module on your site to allow for regular maintenance of this database of information.
For the access to the scheduled live lessons we would follow exactly your proposed designs (it's important that this interface offers the same particular look-and-feel as your own site) and would try to optimize the use of the WizIQ API to make the whole process as seemlessly integrated and efficient as possible.
Finally don't forget that in order to implement the login form to your own site an access system nust be created defining the different access levels and corresponding permissions, and your database will have to be adapted accordingly.
Regards
The Bramfeld Team