Generally, the child must have lived with you for more than half the year. If a child was born or died during the year and lived with you (or in the hospital) while alive, you can treat the child as having lived with you all year. If the child was kidnapped, you can treat the child as still living with you.
If the parents were divorced or separated, then the rules take several pages to explain. If you are really interested, see page 13 of Publication 501:
http://www.irs.gov/pub/irs-pdf/p501.pdf
Yes but you must be able to claim them even though you gave up the dependency. The child must live with you all year.
As long as they meet the qualifying child or relative tests, yes.
If the child lived with you for over 50% of the year (183 out of 365 days) then yes, you can claim the child as a dependent on your tax return, even if they don't live with you now.
The child that the child actually lives with for most of the year can claim the EIC on the child. If the divorce agreement specifies that a non-custodial parent can claim the child on his or her taxes, it does not mean that he or she can claim the EIC on the child. EIC is not granted in court orders. To claim EIC, you must pass the age, relationship, and residency requirements. If the child does not actually live with the non-custodial parent for most of the year than the non-custodial parent may NOT claim the child.
Not on taxes no. The parent the child lives with has the main right to claim the child. But if that parent can't or doesn't want to then the other parent can
Yes if you pay over half of the child support.
over the house yes, over the child...maybe not so much.. specially if the child is not yours.
until the child is 18
As long as you can prove paternity (if needed) and you provide for the child, you can.
If she doesn't live in your household, nothing. If she lives with you, you can probably claim her as a dependant.
You can not both claim her. If he stops claiming her then you can.
If he has no taxable expenses in the child then he cant claim on tax.