Yes.
An illegitimate child can be baptized.
no
yes the child is only once baptized.
No, the child needs to be baptized. Catholicism is not passed by generation, rather by the Sacrament of Baptism.
Yes, a Catholic child should be baptized in a Catholic church.
they werent
Any child may be baptized if there is a reasonable hope that they will be brought up Catholic or in danger of death.
Yes
It is dependant on the country.
It is dependant on the country.
yes if the child accepts Jesus as the savior of his/her life.
Yes, a child can be baptized if his parents are separated, even if they are divorced. Children are not penalized for the mistakes of their parents.