1) haven't seen anything like this in service management API or so. However the rdp file only contains information about the specific instance of the specific service, so you should be able to come up with that information yourself
full address:s:mydemoapp.cloudapp.net
LoadBalanceInfo:s:Cookie: mstshash=MyDemoWorker#MyDemoWorker_IN_0#Microsoft.WindowsAzure.Plugins.RemoteAccess.Rdp
2) not quite sure I understand that correctly. You planning to open an RDP connection from another Azure application?
3) haven't checked recently but there were clients available for Mac and other OS as well. Any RDP client should do, nothing specific to VM Role.
You should have in mind that this RDP is typically meant for administrative purposes, less for end user application access.