It is my personal recommendation that if you have a rental property in another state, you file a tax return there. The primary reason is you have you record of reporting on file with the state.
To answer your questions regarding terms:
AAGI- Arizona Adjusted Gross Income is simply the Federal Adjusted Gross Income (AGI) adjusted for the state taxes. (For example, there may income/deductions allowed for federal that are/are not allowed for state.) This is the amount before any credits, personal exemptions, or standard/itemized deduction. If the only thing you are reporting is your rental property, then your AAGI will be the net profit for AZ from that rental.
AZ Taxable Income is the net profit from your rental minus credits, personal exemptions, and standard/itemized deduction. If your AZ Source Income is a negative number, and your only income in AZ is the rental property, it is impossible for your AZ Taxable income to be a positive number as you posted above.
GI - Gross Income is the total of every dollar received on your rental property before deductions or adjustments. Your AZ Source Income should be the same as your Gross Income (GI) for Arizona.