"3. I want to install surge protection not only on the incoming power
line (which the APC 2200 should take care of), but also on the "dish"
cable. "

A UPS is a poor substitute for proper surge protection, which should be
located at the service panel and have a very short path to a single
point earth ground. There it will be effective because of the short
ground and will also protect all the electrical eqpt in the house.
A secondary surge protection located near the equipment it's intended
to protect can serve as secondary protection or for situations where
whole house protection is not possible, eg a rental apartment. But it
will never be as effective because it relies on the house wiring to get
to an earth ground. And the impedance present between whatever place
it's connected in the house and the earth ground will be enough to
greatly diminish it's effectiveness. Plus, if something does take a
hit, I'd rather replace a $100 surge protector at the panel than a
$1000 UPS.

Unless you live in an area with frequent power problems, like short
outages, or brownouts, or have some mission critical computer
applications, IMO, a UPS is waste of money. And I think a UPS is
pretty usless for any type of TV, which only needs surge protection.

As far as installing lightening rods, if you want to do that, I would
only have that done by a professional. For it to be effective, you
need to have it done right. Plus an incorrect install could be worse
than having none at all.