"Through adding zeroes between the decimal point and the 7 in the string '.7', the number we are representing can be made arbitrarily small." Is this a misuse of the word "arbitrarily"?

Your usage is fine, so long as it's clear that "arbitrarily small" is a feature of the set from which you are choosing numbers, or of the process by which you are constructing numbers, and not of any particular number in that set. This is clear with the context that you give above. It wasn't as clear to me when you wrote that "epsilon is (conventionally) an arbitrarily small number".