Hey,
I happen to be a Christian who's into occultism myself, to answer your question, the Star of Bethlehem and pentagram are two separate things (sort of). The Star of Bethlehem doesn't have the interwoven structure, and most Christians see at as something distinct.
But it did likely originate from the pentagram, several religious scholars think so, and, furthermore, the pentagram itself I happen to know, is referenced in at least one published work "symbols" as being taken directly as is into Christian symbolism even though it is thousands of years older than Christ, for the exact reason that you mentioned: the wounds (though usually the 5 wounds I've heard correspond to the hands, feet, and head--crown of thorns--but the center chamber of the pentagram can be taken as the wound from the spear of destiny). Thus, ancient christians it seems accepted the pentagram for a time directly as is, before the church was powerful enough to worry about "cleansing" its' lands of users of magickal arts, to whom the symbol belonged first. Though for the afforementioed reason, I think Christians have right to it as well.
The pentacle however, doesn't have a direct Christian parallel, because it is a pentagram enclosed within a circle, and is a distinct symbol, separate from the pentagram itself, it has different meaning, it specifically represents only the element of earth in many systems including kabbalistic and ceremonial high magick (both of which have major judaic/chrsitian influences) and the tarot. This is likely because in high magick, as well as in natural magick (paganism, withcraft etc.) the pentacle is actually one of the 4 major tools of magickal practice, it is supposed to connect mostly with earth, but it is, more specifically, a representation of all the magician/witch believes to be in existence within the macrocosam (both physical, but more importantly non-physical universe). It is basically equivocal to the computer's key board when your writing, all the letters and notations are there, but it takes the writer (magician) to combine them and get results (perfom magick). Thus, as it is a minature representation of everything, it also includes the other elements too (hence the pentagram) but as it involves the manifestation and physical representation of these aspects, it is still primarily earth. As it is all aspects viewed through the modality of earth.
As to the 5-pointed start of fellowship, I've never heard of that before, but you're right in that in description, in does sound like the inverted pentagram, however I can understand Christians not liking that one, as it has meant both in magickal tradition and elsewhere the subversion of divinity, and as per the wounds of Christ interpretation, the subversion of the divinity of Christ and the sacrifice he made. There, to my knowledge, was only ever at least one (possible 2 or 3) instances in history where a Christian was crucified this way: one of the saints wished to be crucified upside-down because he felt he wasn't worthy of being killed in the same manner as Christ, and thus, it is somewhat in keeping with the afforementioned interpretation as he wasn't trying to subvert Christ, but he was trying to show he was below him, below the divine, and that to be crucifed normally (in his mind) would've been subversive, or insulting to God.
I think that about covers it.