Q1 - How many MD systems are needed? One per TV?
Correct, though you can do some tricks to move audio/video to multiple rooms the best solution is a MD at each location.
Q2 - How many cable tuner cards are needed?
One tuner per MD, now there are cards/usb devices that have multiple tuners in one. The HDhomerun has 2 per, so 3 of those. Do not forget that with tuner cards its 1 per MD PLUS one for every scheduled recording you have. To stream to 6 MDs at once and record 2 shows would be 8 tuners.
Q3 - The core system, what type of power is needed if I wanted to have all TV streaming at once? (Not that it would happen.)
A valuable lesson about "power", think in terms of I/O and eliminate bottlenecks in your core hardware and you will be very happy with less than TONS of ram and proc power.
Q4 - What is the best way to control the TVs, BluRay and other devices? IR or through service ports?
I personally am a fan of RS-232 (service ports) but to ask for devices with it in an electronics store always gets deer-in-the-headlights look. IR works, if the device comes with a remote then lmce can send it commands. If you want to try alternate means of connection such as ethernet and usb then I am sure you will find the help you need here.
Welcome to LinuxMCE. I look forward to hearing how your system comes along. One last note, you WILL use more storage than you thought possible. If you want a impressive DVD collection, HD recordings, a couple thousand songs the storage space goes fast. My very small lmce setup already has more TB than my last corporate jobs' server. If you are wanting to get the core/MD/AV all going at once I would go ahead and either get a large oob NAS or build an expandable one. Keeping my storage on my core is one of my regrets and will have to be resolved before I run out of powersupply or case room.