No. They only have tuners for DirecTV and have no MPEG encoders
(they don't need them since the DirecTV signal is already digital) so
can not record from any source except DirecTV. Their RF (non-satellite)
input can only pass an RF signal to the output when the box is in
standby mode.
The exception to this is the HD DirecTiVo which can record from
antenna as well as DirecTV. Its my understanding that a DirecTV
subscription must be maintained to have the program guide data needed
to record over the antenna.
Not without running another line from a multiple-LNB dish or from a multiswitch connected to a multiple LNB dish. If your dish only has one cable coming from it it's single LNB and would need to be upgraded to dual. If you have a dual LNB dish but another receiver is using the other feed you'll need to install a multiswitch. YOU CANNOT USE AN RF SPLITTER on a satellite signal. See unixadm's post LNB, Multiswitch, and DirecTV Signal FAQ's
From wayne: First, if there is any way you can run a second cable from the dish/multiswitch, that will be easier and cheaper, so try that first. If the wiring is impossible, you can combine two satellite cables onto one wire in some cases. See discussion here to see how this can be done: Wiring question I've not found a viable answer to...