Yes.

Yes.

http://www.mythtv.org/wiki/Hardware_Requirements

Well not quite. Every computer has a video card but always in laptops and
sometimes in desktops it is part of the motherboard.

Not all laptops have embedded graphics, there are those that use a
mini-pci type slot for a separate card with its own on-board memory
just as in a desktop :-) Some even allow you to upgrade this but the
upgrade path is pretty limited as physical shape and size of the card
is specific to the laptop model. Usually only the option of NVidia or
ATI cards for those preferring one over the other.

I stand corrected, but my point was that the other person should know that
she did have a video card even if it was not obviously present. In my very
limited experience of half a dozen portable computers every one had
integrated graphics.