Lots of baby words are shared amongst languages even if they're not related. The most obvious one I see are the variations of baba, papa, dada, etc for dad.
My iraqi friends say baba and arabic is certainly not originated from latin.
There are certainly some Latin loan words in Arabic; that part of the world was well within the Roman sphere of influence for a long time. For instance: the Arabic ṣirāṭ and English street both come from the Latin word strata.
No, but several of the earlier languages in Anatolia did have Into-European roots as did some of the surrounding languages, such as Persian. It could easily be a loan word.
*kakka-
also kaka-, Proto-Indo-European root meaning "to defecate." According to Watkins, "imitative of glottal closure during defecation."