Do far away planets reflect light in the same way our moon/earth reflects light?
The short answer is yes, the outer planets of the Solar System reflect light in much the same way that the Earth does, but exoplanets are too far away for us to see clearly.

If you looked at Jupiter, you would be able to see the same colors that show up in Juno's photographs.  Even though the sun is less bright out there, it is still bright enough to illuminate the surface.  At Earth, the sun's irradiance (its intensity) is ~1361 W/m$^2$.  At Jupiter, the solar irradiance is ~50.26 W/m$^2$.  This is about the intensity of a common lightbulb.  Going further out, the solar irradiance at Pluto is ~0.873 W/m$^2$.  

Now, this is not a very high intensity.  When you move away from the sun, things get darker and darker.  However, we have special instruments to counteract that.  We use telescopes to gather up large amounts of light and focus them, so that we are able to get a clear picture.  That is how telescopes work.  We have pictures of Jupiter from the Earth, most notably from the Hubble Space Telescope, and you can see that they are, indeed in color. (The black dot in the middle of the Great Red Spot is the shadow of Ganymede, one of Jupiter's moons).



There are plenty of resources online to learn how telescopes work.

As for planets outside our Solar System, we can't actually get pictures of them.  Any images you've seen of exoplanets are actually drawings made by artists.  They're so far away that we just don't have the resolving power to see them clearly.