Education

Yes, you can still claim an education credit, even if you did not pass the class.  There is not a requirement to pass the class, the requirement is that you are enrolled in the class at least half time. Since you were enrolled full-time, if you are otherwise eligible to claim an education credit, then you can still claim one. 

Yes, you can still claim the credit even if they did not issue you a 1098-T. 

As for whether they are required to issue you one, when you do not pass the class,  This is not one of the specifically stated reasons for a school to not issue you a 1098-T, however, as stated above, if you are eligible, you can still claim an education credit without the 1098-T. 

The qualifications of the credits are below:

 Lifetime Learning Credit

• You can take this for an unlimited number of years
• Twenty percent of expenses up to $2,000
• Non-Refundable meaning this can reduce the amount of taxes you owe, but if your tax liability is less than the LLC, your tax will be reduced to $0 and the rest of the credit is lost. 
• Cannot be claimed as a dependent on any one else's return
• As a Married couple, your income must be below $160,000 for the full credit and below $180,000 for a partial credit

American Opportunity Tax Credit.

• Available for the first 4 years of college
• Max amount is $2,500 per student
• Be enrolled in a degree or credential seeking program
• Not have a felony drug conviction
• Be enrolled at least half time
• cannot be claimed as a dependent on anyone else's return.
• As a Married couple, your income must be below $160,000 for the full credit and below $180,000 for a partial credit

Tax Deductions for Voluntary Interest Payments on Student Loans

What Are Education Tax Credits