Él conoce a las mujeres
Apparently I can write "He knows women" as both "Él conoce a las mujeres" and "Él conoce mujeres". In the first case, is there no distinction between he knows women (in general) and he knows the women (referring to some specific women)? In the second case, why is the "a" unneeded? Do the two actually have a difference in meaning as in the first refers to some specific women whereas the second does not? Sorry for the mess of questions, help appreciated!
The two do have a different meaning, actually. In the first instance, where you're requiring an "a", you're talking about specific women. This is why you're required to use a personal preposition. In the second case, you're talking about women in general, which is more of a concept statement. Because there are no specific women involved, there's no need for the preposition.
This may assist in the explanation, but it will also help later on, I think. "a", when used in this manner, can also imply a personal relationship with somebody. For instance, "Veo el hombre" means "I see the man," and "Veo a mi hijo" means "I see my son," but the latter implies a personal relationship with the object, while the former indicates that the man is not familiar to the speaker.
The object is always specific when you put a Definite Article in front of it. The "a" is just a requirement to introduce a direct object that is a person or treated like a person.
Well, ACTUALLY, there aren't strict rules stating when exactly to use prepositions. Although there are some rules, preposition usage does vary from place to place and even from person to person. It's frequently more about linguistic customs or tastes than about grammatical rules. Thus, don't worry too much about it, Spanish speakers will understand you either way.