I wouldn't think it's so much a matter of hybrids or mutants being 'allowed' or not ayah (in a RP context), but you'll of course only have the available races to choose from when creating a character. Although if you wanted to RP that you're from mixed heritage I guess you could say anything you wanted really. Whether or not it's realistic or believable would be another thing.
I'd guess in a realistic context you could only mix the same species and subspecies, ayah. For instance my father's human and my mother's Corellian (a human subspecies so to speak), a mixed heritage but still making my species being human make perfect sense (or I could have been Corellian and said same thing).
I think it takes more than simple visual simulaties for it to be realistic, for example Humans and Twi'leks are completely different species/races of beings despite having some general physical similarities. In the end I guess it's up to you - although people would probably just look at you funny if you claimed you were half hutt, half hapan you know, but I'm sure it's probably been claimed by someone. :)
Regarding cybernetics I dunno. I know nothing of such technical things, although Jaxom Sky did say his eye piece thingy really hurt to get fitted, ayah. D: