Do far away planets reflect light in the same way our moon/earth reflects light? Here’s a scenario:

Say you’re up in space and you’re far enough way that you can see the planet earth. Whilst looking down, you can see  blue sky, blue water and green land and white clouds and darker shades of different colors. This is because our sun is reflecting light off our planet that we can see these colors. 

Now you’re up in space and you’re far enough way that you can see the planet Jupiter. If you looked, would you be able to see colors in the same way we’ve seen from Juno’s pictures. I see red, white, orange… The sun is so much further away, how can the colors we see be just as bright/visible to us? The same question holds true for planets outside our solar system. They’re so far way from there light source, yet I can see colors on them. How come the distance of the light source doesn’t affect the brightness of the colors I see on these planets? 

Like if I was to turn on a light bulb in a huge dark room and shine that light in the middle, the surrounding areas would be much brighter than the furthest point of that room/and at some point there would be no light reaching an even further point. 

Bear in mind I’m a basic idiot when it comes to this stuff.
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.