It all depends on how nice your installer is. For the tivo hookups, as an HSP employee I am mandated to accomplish complete system integration. If your electronics functioned when I arrived, they must do so equally as I leave. Many technicians though, both contractors and HSP employees are completely unfamiliar with tivo units and you may or may not have success in this regard. There is no training for these that we receive.
If you are getting an H20 installed, they should be installing a 5lnb kaku dish. They will not give you a choice.
Running a separate line from a receiver to another television is quite acceptable per DirecTv, but is definitely not part of standard installation. My office charges $70 for slave lines, but I've often done short ones for free due to the hassle of the electronic check authorization process we have to go through.
As charper said don't be surprised if you end up getting rescheduled. If you get a contractor who is only interested in hammering through installations, they may refuse to do anything custom as they won't have the time available. You will likely then get rescheduled to an HSP employee.
edit: addendum: Also, as I'm sure your ota antenna is headed to the h20, remember that the lines cannot be diplexed for the 5lnb. The installer will need to run a second line for the antenna. Going through exterior walls is standard, but if the tech has to wallfish to an interior wall that is extra. Typically $35 for a wallfish.
edit: reread: Also, for the dual tuner tivos recording one show and watching another. As the tivo will now be fed by the satellite tuner, and each of the boxes you are having installed are single tuner units, this will simply not be possible. The only option here would be to feed the antenna line to your tivo, and this would allow viewing ota broadcasts while recording satellite, or vise versa. Either that or you'd need a second satellite receiver to feed each tivo tuner. That becomes complicated though.