Does BizTalk Services offer HL7?
No, BizTalk Services doesn't have this capability yet.
Do we have to pay for BizTalk Services to use Hybrid connectivity with HL7?
No, BizTalk Services is a specific capability in Azure for integration, Hybrid connectivity is the act of connecting something in the cloud to on premise services, not the same.
Can we use Hybrid connectivity to securely connect between our on premise services and between various on premise data centers of our customers?
All traffic between Azure data centers is encrypted.
All traffic between Azure data centers is in dedicated circuits and not routed over the internet.
Azure network traffic supports both server to server, virtual network to virtual network, azure to on-premise VPN connections, and significantly more advanced capabilities than a standard VPN connection like ExpressRoute.
All traffic between services running in data centers is monitored, tracked, and controlled using advanced networking security that isolates the systems from each other and from the internet.
A good starting document is the Windows Azure Network Security white paper that goes into deeper detail.
In summary, Hybrid connectivity takes advantage of Azure Network Security and is a good solution for HL7 connectivity to on-premise services.