Can everyone dissociate?

Dissociation comes from dis-association.
Dissociation is a natural way of coping with acute trauma or stress. Dissociation means an insufficient integration or a fragmentation of personal experiences or perceptions, emotions, sensations, and thoughts, but without the loss of identity. Stating that highway trance, daydreaming etc. is also dissociation is not right, cause one is still in contact with reality ('reality testing').

Dissociative experiences are often seen as a result of serious psychological trauma (f.i. a serious car accident, when someone is told he/she has a life thereatening disease, natural disasters, war trauma, hostages, kidnappings etc).
Dissociative experiences are also seen as a symptom or phenomenon in different personality disorders. One speaks of a dissociative symptoms when it is seen in other disorders, like schizophrenia, autism, borderline etc.

Dissociative symptoms can become a dissociative disorder (pathological), when it causes severe suffering or limitations in one's personal life and when it hinders social and personal daily functioning.

Is - DID (former Multiple Personality Disorder) the same as a split personality?

Splitting and dissociation belong to the same phenomenon. It's an old term and mostly used in populair media and books.
With DID there are so to speak walls created between the parts of the personality (splitting into fragments), together with the traumatic experiences which are likewise split. This is not to be confused with splitting as in schizophrenia, where certain brain structures do not function in the usual way.
Extreme DID was often misdiagnosed as schizophrenia.

Because woman mostly turn their aggression inside and most men outside, it is plausible that the first group mostly ends up in the psychiatric system and the second in the criminal system. Because of that it appears that the disorder is most frequent in woman, but one can speculate that it may be equally common among men.

No, you don't have to worry about that. It is important that young children develop their fantasy and sometimes an imaginary playmate is part of that. In fact you should have something to worry about if your child doesn't show any kind of fantasy play.

Only if your child shows disturbing behaviour (regarding an imaginary playmate) like for instance: not speaking for days, abnormal fighting and so on should you really be worried.

Yes! Because of the complexity of DID and the necessity of going slowly and safely the (psycho)- therapist has to be a mature person with previous experience of successfully treating DID or severe psychotrauma. This is crucial, because the symptoms of DID are difficult to treat and some of the causes so deep that they call for a very capable psychotherapist. This can only be done gradually, as the patient feels increasingly confident, safe and able to integrate each new portion of their personality into a new understanding and experience of his or her self.
There is a lot of confusion about working on traumatic experiences in therapy. It's not necessary to relive the trauma, but the expression of intense affect concerning the trauma, which is important to work through in therapy.

On the one hand this has to do with the fragmented nature of a DID.
On the other hand, war traumas and natural disasters are a collective trauma, meaning that more people share (more or less) the same kind of experiences and they can talk about it with each other. Besides that these are often given media and public attention for it. This is not the case with child abuse, individual experiences where in most cases the perpetrators also threaten children with violence and death if they should speak out to others. And because they are still children who depend on the family they live in, it makes it even harder for them to tell the outside world.