Enter the kids, as dependents, in the personal info section. Then carefully follow the interview to indicate that the non-custodial parent is claiming them. That will allow you (and your spouse on a joint return), as custodial parent (the parent the children live with for more than half the year) to claim the EIC. You can only do this on a joint return. Filing as Married Filing Separately disqualifies a taxpayer for the EIC.
There is nothing to claim on a federal return for paying off your house. What is it you think you get? If this is a state tax benefit; you should ask a new question and identify the state.
