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 1098-T can be used as one means of proof of enrollment if a tax credit is claimed, and the information on the form may be useful in determining whether a tax credit of the Hope or Lifetime Learning credit may be claimed on Form 8863.