Regarding your first question that might be possible. If you registered for credits for only Spring semester of 2010, then probably the university sent you bill during December of 2009. If that is the case then the tuition fee for SS2010 will be in 1098 of 2009, because you were billed in 2009 even though you might have paid it in 2010. If you paid the tuition fee in 2010, you are eligible to show that in your tax return.
Hope that helps

Sparty