Q1) Is this correct and should I only count 2019's charges? If so, do I use the "what if this is not what I paid to this school" entry to reduce the 1098-T box 1 amount?
A1) Yes
Q2) I also did this last year... Should I amend last year's taxes to eliminate Spring 2019 and then include Spring 2019 & Fall 2019 on this year's taxes?
A2) Yes, but only if it makes a difference. It only takes $4000 of qualified expenses to get the maximum American Opportunity Credit. So, for example if the 2018 1098-T had $10,000 in it and after adjusting it woulda only had $5000, you don't need to amend. Your bottom line will remain the same.