I don't believe you can record directly to EHD. It would have to go on the internal drive, then manually be transferred over. Not necessarily built in Internet, but they offer DishNet which is satellite internet. Depending on location it is either via sat or HughesNet. Likely HughesNet as Echostar bought them in 2012, and expanding on Dish. The Hopper and SJ can do a total of 5 tuners. With an extra hopper, you get 6 tuners. There is a limit to how many Joeys can be linked to a single Hopper, and I beleive it it 3 or 4. You'd have to get clarification on that from a DIrT member as those limitations can change. With 4 or 5 TVs, you're better off with 2 hoppers anyways. They would work independently of one another, but the Joeys can link to either, and you can watch recordings from any hopper or Joey throughout the house.
If you are watching a live show, change the channel, then come back to it, you will lose the playback. If you pause it on multiswap, however, it will retain the info up to an hour. You can use multiswap on 4 shows, but each uses a tuner(so 2 of them would have to be locals, such as during Football season) or the SJ. Here is one not mentioned, only the Hopper and the soon to release 4K Joey have the PiP ability. If that's important, know which room the hopper is in.