How does science reconcile the paradox of meeting yourself in the past during time travel?

For time travel to work as promoted by most sci-fi writers and movie makers, you can go back in time and interact with your past self. How does science reconcile:

• Your present life force/spirit will be occupying the same space as your past life force/spirit. How do they both reside in the same time continuum at the same time?
• If a person went back in time and their past self, thought your present self was an intruder and pulled a gun on his/her present self, who in the struggle not to get shot, accidently shoots the past self, putting a bullet in his/her own past self’s brain. How would he/she be able to be in the future to go back into the past if one kills their past self?
• Seeing a parson who is in the future can to go back in the past, does it mean no matter what, he could not kill his past self even if he wanted to?
• If a person when back in time would he is a mere observer as a latent imprint in another dimension unable to affect his/her past self in any direct way?

How would these seemingly contradictions are paradoxes be solved or reconciled scientifically?