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.
You can only claim a qualifying-child exemption if your child lives with you for at least half the year. The IRS offers a number of exceptions for this test. If your 20-year-old is at college eight months of the year, you can still claim him; if he stays with relatives while you're on military duty, he still qualifies.