You are not a citizen until you are sworn in. If you are denied because of failure to pass the English or the civics test, you will be automatically rescheduled within 90 days. If you are not approved for some other reason, you may be given time to overcome the problem.
For 2009, the American Opportunity Credit--which is a variation of the Hope Credit--will be allowed for 4 years. For years before and after the new credit is allowed, the Hope credit is supposed to be for 2 years.
This still remains the parent's choice. Provided the parent has lived with the child for at least six months and one day, the parent can always choose to claim his or her child for purposes of the earned income credit. In a tiebreaker situation between two unmarried parents, the tiebreak goes to the parent who lived with the child for the longest.