I am trying to isolate pure carbon in its elemental form. Are there any decomposition reactions or other easy to carry out reactions to yield solid carbon? and in the case that it is isolated, does it start reacting with other elements in the air?
A classic reaction to yield carbon is the dehydration of sucrose (table sugar) with concentrated sulfuric acid: Put some sugar in a beaker, carefully add sulfuric acid and watch a voluminous "snake" of porous carbon (blow up due to the steam released during the reaction) from the beaker.
You'll find lots of videos on this on youtube or other platforms.
Note that this is performed with concentrated sulfuric acid! If you decide that you must do this at home, protect yourself (googles, gloves, lab coat) and keep the sulfuric acid locked away.
But there's a more simple way to yield carbon:
Hold a spoon (with a long handle) into the flame of a candle. The black stuff that deposits on the spoon is carbon. Play with the distance for optimal results.
As far as the reactivity of carbon is concerned: There's no danger in that! Millions of people stockpile carbon in the form of coal at home in their cellars or sheds for heating.
And actually, this points to the easiest and most safe option: Don't perform any reaction at home and grind some charcoal or anthracite coal instead.
You should be able to drive off water from a pure carbohydrate (like sucrose) simply by heating it enough. Think of it as a very simple example of destructive distillation.
If you prefer something a bit more exotic, you could ignite a magnesium strip and drop it onto a block of dry ice. The magnesium will combine with the oxygen, leaving carbon soot. I'm not sure how easy it would be to collect that soot, though, or to separate it from the magnesium oxide co-product.