Azure Service Bus provides a lot of different capabilities, but the one you seem to be most interested in is relaying.
Please consider this excerpt:
The Service Bus Relay service enables you to build hybrid applications
that run in both a Windows Azure datacenter and your own on-premises
enterprise environment. The Service Bus relay facilitates this by
enabling you to securely expose Windows Communication Foundation (WCF)
services that reside within a corporate enterprise network to the
public cloud, without having to open up a firewall connection or
requiring intrusive changes to a corporate network infrastructure.
The Service Bus relay allows you to host WCF services within your
existing enterprise environment. You can then delegate listening for
incoming sessions and requests to these WCF services to the Service
Bus running within Windows Azure. This enables you to expose these
services to application code running in Windows Azure, or to mobile
workers or extranet partner environments. The Service Bus allows you
to securely control who can access these services at a fine-grain
level. It provides a powerful and secure way to expose application
functionality and data from your existing enterprise solutions and
take advantage of it from the cloud.
I think that excerpt answers your first and fourth questions.
To answer your second question, if by "ordinary connection" you mean a connection utilizing HTTP or TCP protocols, then yes.
To answer your other questions, yes, it is always helpful to understand--with at least some degree of depth--a technology you are utilizing, especially if you want to avoid common mistakes and maintain decent performance. While you do not need to use WCF to connect to an Azure Service Bus, if you are planning on using WCF in your project in conjunction with Azure Service Bus relaying, then naturally it would be of great benefit for you to understand that technology. I recommend you follow a MSDN "Getting Started" tutorial.