Re the recordings ..and assuming your talking about a “Local” network station , if you moved out of the spot beam of the local network channel say NBC on KEEE and change the local to the new NBC station KERR ... no it won’t record .. it’s looking for KEEE and can’t find it. You need to create a new scheduled recording for the new NBC channel. This doesn’t occur with HBO or STARZ Etc as those channels don’t change.
That’s one reason people use , and pay for the dns stations out of LA.
I don’t know why it wouldn’t record national channels .. ( like STARZ ) mine does no matter where I move.