Please don't give me any spoilers for the new BSG, but I do want to know whether or not the character known as Six in new BSG was in original BSG? if the answer is yes, then what role did she play (as in how did her character act)?
Six was not in the original BSG. Her character was first introduced in the 2003 miniseries.
In the original BSG there are no skinjobs (cylons that are nearly indistinguishable from humans). There are humanoid cylons, such as Andromus, which superficially appear as humans, but these are entirely mechanical beneath their artificial skin.
No. Cylons were machines in the original BSG, period, end of sentence.
However, as this was pretty expensive, the producers had intended to introduce human-looking robot Cylons in the second season. The show was cancelled before then.
Six nor any other humanlike cylons were part of the original BSG. Even though the original BSG was not very consistent with the cylons I don't remember any work where completely humanlike cylons existed.
As for the inconsistency: In the series and most films the cylons seem to be an android like race while in the books it is mentioned that the "original" cylons are an alien race, while the android like cylons are only a sub group of their warriors (the book with the giant weapon on the ice planet makes a few references there).