You do not have to use charcoal but it's a very good idea. I do use the fish tank charcoal, you can buy it in small containers at any pet store.

Iffy on the moss. If you 'll give it the same light in the terrarium it's getting outside it'll thrive. Often the other terrarium plants want more light than the moss does.

The amount of light depends on what you've planted.

Charcoal is completely unnecessary. Don't bother.

Are you looking at this as a temporary terr that will be redone every 2-3 months or something more long term. If the former, you have lots of options as you can treat the plants more like cut flower arrangements -- displays of ephemeral interest/beauty. If more long term, your options are very limited.

Is the plant you are referring to Pilea involucrate? If so, that plant will very quickly outgrow your little globe. In a terr that size, you could try instead:
* micro-mini AV (I rather suspect that even a typical mini AV will likely get too big too fast)
* mini Drosera (sundews)
* mini Pinguicula (butterworts -- you'd have to plan on the Mexican pings, I think)
* mini Utricularia (bladderworts -- terrestrials probably best ones to try)
* moss (with stones, tree branch, etc to create a mini scene)

TtC is spot on regarding light -- that will depend on just what you decide to grow in it.