Welcome! Firstly, I'll assume you are in the US. Term: core/hybrid - is the central "master" LMCE server that is dual-homed and sits between your Internet connection and the rest of your home network. A "core" specifically is the master server only. A "hybrid" is a core plus a Media Director (MD) on the same unit. You only need one or the other, of course, and most people choose hybrid. Media Director - this is the component that actually plays media in a particular Entertainment Area. You would normally place one of these in each location that you want to be able to control/play media independently. One is included when you install in hybrid mode. The other Media Directors can be very small units and run diskless by PXE booting off the core/hybrid server. Take a look at the ASUS Eee Box B202 for instance.
1. I would strongly recommend the HDHomeRun network tuner. It is pnp out of the box for LMCE, you can place it anywhere on your network and LMCE will find and install it, then you can share out either of its 2 HD tuners to any Media Director on the network.
2. I would suggest keeping your media separate from your LMCE server or MDs, either on a general purpose PC with big drives, or a dedicated NAS. Its more convenient this way for several reasons.
3. There are dozens of remote options, so I won't detail them all here. The Fiire remotes are very good if you can get one and some dongles (they have gone out of business, so you will need to look second hand), and the stand out performer is the WebDT 366 wireless web pad that tkmedia sells. Great units!
4. Depends what you want to achieve... a true LMCE system means an MD in each location, as described above, and that means a simple PC to certain hardware specs. This way all the MDs will be able to interact with each other, control each other, present a common house-wide media/control interface, bounce media back and forth between them in real time, split/duplicate media streams, etc.
5. X10 is pretty old and clunky. It works with LMCE, but given that the technology is over 30 yrs old, not surprisingly it is slow, unreliable, and not very feature rich. It is however, cheap! For the US a better alternative would be Insteon or ZWave, both of which have pretty comprehensive drivers in LMCE, are fast, reliable, bidirectional and have far more features.
6. I believe that most IP Cameras will work because LMCE just hooks into whatever URL they provide their images on (stills). The Motion add on provides the security detection....
For details on network setup (which is critical) http://wiki.linuxmce.org/index.php/Network_Setup
Also read the wiki FAQ