Can an unmarried, pregnant tunisian muslim woman keep any children she has with a western man or will they be taken into care when she gives birth? Does the western man have any rights, can he keep the children?

Depends on which country that you're implying the western man to be from and where the children are born.

If the western man is from England?
The children are to be born in Tunisia.

Then I suppose this would go by Tunisian law.
I found this stuff on a sight:
" When one of the parents is Tunisian, a child is considered Tunisian regardless of the child's place of birth or whether the child had acquired the nationality of another country."
And
"The parent can request that a foreign child custody order be recognized in Tunisia, but enforcement will result only if the custody order conforms with Tunisian child custody law. Therefore, as a practical matter, foreign child custody orders are not generally recognized in Tunisia, and the parent must seek legal representation in Tunisia and file for custody in Tunisia."
And
"When a child custody dispute arises between parents, one of whom is a Tunisian, the courts determine which parent is awarded legal custody of a child. Child custody laws in Tunisia are codified in the Child Code Law 67 of the Code du Statut Personnel Tunisian. Tunisian judges take into consideration the welfare and protection of the child and the eligibility of the parent seeking custody."

I found this at a US website: International Parental Child Abduction Tunisia (http://travel.state.gov/family/abduction/country/country_531.html)
But there is a board that may help you out a bit more at Kids with tunisians - Tunisia.com Community (http://forum.tunisia.com/general-discussion/1333-kids-tunisians.html)

Good luck!