Are there innate differences between men's and women's behavior? A stereotypical man is aggressive and competing.
A stereotypical woman isn't aggressive and tends to cooperate rather than compete.

A stereotypical boy have toys like cars and plastic soldiers. 
A stereotypical girl have toys like barbie dolls.

So far I believed this is merely the result of the social conditioning, where boys taught to behave like a men, and girls are taught to behave like a women.

But it seems I need to think it again. I recently read this article about the girls in Salinas. They have a weird genetic disorder that makes boys born like a girl and they won't grow a penis until the age of 12.

The interesting thing is that it seems not only their penis grows but also there is a change in behavior (quote from the article above):


  A little girl named Carla is currently going through the same
  transformation, aged nine. Despite being brought up as a girl, his
  mother noticed that from the age of five he was more inclined towards
  the rough and tumble play of little boys. He has recently had his hair
  cut shirt after wearing plaits for years.


Also there are examples of transgender people who have gender dysphoria often describing themselves as a "woman who is lost in a man's body" or vice versa.

Is there any serious scientific research that proves / disprove these perceived differences in behavior?
This is still a matter of fierce debate between the essentialist and cultural camps.

There is little argument that gender differences are shaped by culture, but there is now a growing evidence supporting the hypothesis that gender differences are also partly the outcome of biological disposition.

Much of such biological disposition is the outcome of hormonal influence. Given that such influence was demonstrated even if prenatal, and that the instructions to the postnatal generation of hormones is coded in our DNA, you can argue that such influence falls into the definition of innate.

You may wish to start with these papers:


Alexander, Gerianne M., and Melissa Hines. "Sex differences in response to children's toys in nonhuman primates (Cercopithecus aethiops sabaeus)." Evolution and Human Behavior 23.6 (2002): 467-479.
Hassett, Janice M., Erin R. Siebert, and Kim Wallen. "Sex differences in rhesus monkey toy preferences parallel those of children." Hormones and behavior 54.3 (2008): 359-364.
Maestripieri, Dario, and Suzanne Pelka. "Sex differences in interest in infants across the lifespan." Human Nature 13.3 (2002): 327-344.