1. The HD receivers and HR24 HD DVR have their own satellite tuners, so yes, you can watch Live TV on any of those, regardless of what the Genie DVR's five tuners are doing.
2. Same answer. The Genie DVR's tuners have no impact on what the HD Receivers and HR24 is doing.
3. Not sure what you mean by "compatible", but I think yes. With Whole Home DVR sharing you can view any of the Genie DVR's and HR24's recordings on any of your other DVRs, Receivers, or mini clients.