If we can "see" all of the planets, can we see the Lunar Rover, etc.
on the surface of the Moon?

Hello.

No, we cannot currently use telescopes to see the various objects left
behind on the moon. Even the powerful Hubble Telescope is incapable of
picking up small objects on the moon.

Here is NASA's explanation:

"Can Hubble see man-made objects on the moon?

There are a couple of problems with HST viewing things on the moon:

1. Size: An object on the moon 4 meters across, viewed from HST, would
be about 0.002 arcsec in size. The highest resolution instrument
currently on HST is the FOC, at 0.014 arcsec. That would work out to
being able to resolve something about 300 ft across on the moon. So
anything we left on the moon cannot be resolved in any HST image. It
would just appear as a dot -- except see next point.

2. Motion of the moon: The HST pointing system is designed to hold it
quite motionless relative to the distant stars -- but the Moon isn't.
In 1 second of time, the moon moves over 0.5 arcsec. The shortest
exposure time any of the HST instruments offers is 0.1 sec -- so an
object we left on the Moon would appear more blurry."
Source: NASA Hubble faq
http://hubble.nasa.gov/faq.html

Also see the answer to this question on howstuffworks.com:
"Is it possible to see (with a telescope) the stuff left behind on the
moon by the Apollo astronauts to prove whether the missions were
real?"
http://www.howstuffworks.com/question188.htm

Also see this explanation:
"q: Is it possible to see the manmade objects such as the lunar
lander, and rover on the moons surface? I am working on a school
project and nobody seems to know the answer to this. (Steve
Schwertfeger)
a: Even the most powerful telescopes, such as the Hubble Space
Telescope, the Keck telescopes on Mauna Kea, Hawaii and the European
Southern Observatory at Cerro Paranal, Chile are unable to resolve
anything as small as the Apollo vehicles at the range of the Moon.
Hubble's threshold, for instance, is around 85 metres across. However,
in theory the long shadows cast by the landers at sunrise and sunset
could be visible, though this has not yet been tried."
Source: inconstantmoon.com
http://www.inconstantmoon.com/qna_obsn.htm


search strategy: telescope, "objects on the moon", "left on the moon",
nasa, rover

I hope this helps.

You might want to look at:
http://answers.google.com/answers/main?cmd=threadview&id=19030
How could I go about building a telescope such that it would be able
to clearly view the US landing sites on the moon?