"separate”, “divide”, and “split” are near synonyms, though "separate" often implies something that can be temporary. Eg: "the pirates divided / split the treasure" implies that each gets to keep his share forever. "The mother separated her fighting children" implies that they will be kept apart only until they are no longer angry, not forever. "My girlfriend and I have separated" often implies that they might get back together; "my girlfriend and I split up" implies that it is permanent.
Spread is completely different. Unlike the others, it can never imply that one thing is now two things, only that the ends of the one thing are futher apart. When an army spreads out, it is still one army, but each soldier is farther from eeah other soldier. When you put a lump of butter in bread and spread it, the same amount of butter covers more of the bread. When I spread my arms, i am holding them further away from each other.