"A lot of faiths have origins & influences, can you name them all?" I don't think it's possible to name all of them and you certainly haven't on this quiz... religions are massive collections of memes, stories, traditions, laws, texts, etc... and many of the more prominent ones have roots stretching back into antiquity if not prehistory. Certainly many of the religions and beliefs that influenced Judaism, Buddhism, etc. have been lost.
and since you had various pagan traditions in other places listed by country or culture, it's a little hard to guess simply "paganism" by itself for Islam. Muhammad's cult was influenced a lot by the various pagan traditions of Mecca and Arabia, though. As well as by Syriac Orthodoxy and the Nestorians, among quite a few other things no doubt.