I read an older article where they talk about species being strictly monosexual as opposite of being hermaphrodite, etc . After an extensive googling and reading about how everybody has to be at least a little bit homosexual, I am still not clear about this. Is monosexual still a valid term to be used in biology? If not, what is the correct term referring to a species that has separate sexes over the entire life-cycle?
I suspect "monosexual" is a term recruited in sociology, psychology and/or medicine. I haven't ever heard of it in application to biological questions. It's a behavioral habit and doesn't seem to be directly related to the (biological) opposition "separate sexes" vs "hermaphroditism".
Animals can either be gonochoristic (separate sexes) or hermaphroditic. If an animal species reproduces without gametes it's called asexual (in animals asexual reproduction is rarely the only way of propagation), and if only females are present which give birth without fertilization, they are called parthenogenetic.
In some cases different modes of reproduction are utilized by different stages (alternate generations) or even phases (larva vs adult, young vs old). In other cases in populations coexist males and hermaphrodites or males and parthenogenetic females.
Mammals, including humans, are (nearly) perfect examples of gonochoristic animals: only a male and a female together can produce offspring. If someone is homosexual (it refers to behavior only), he is a dead end in this respect.