The LNB will be replaced in the dish (maybe). Everything else is good. I would absolutely have the whole-home option, that way you can watch recordings from either location on the other one. You'll end up with 7 tuners rather than 4 which will certainly help resolve the conflict issue.
The HR34 will go where the HR20 is, it will connect to the internet, and the HR21 will also be connected via the coax networking from the HR34. No additional wiring needs to go to the HR21 location.
The HR34 will go where the HR20 is, it will connect to the internet, and the HR21 will also be connected via the coax networking from the HR34. No additional wiring needs to go to the HR21 location.