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.
The credit is bigger, covers more years of college, and helps more taxpayers. The American Opportunity tax credit, previously called the Hope College credit, is valued at $2,500 for 2014, up from $1800 in 2008. Because a tax credit reduces your tax bill dollar for dollar, this basically means Uncle Sam will give you up to $2,500 per year for each qualifying college student in your family.