You should read IRS Pub 970 on Tax Benefits for Education to get a good feeling for how this stuff works. By "stuff" I mean the taxability of scholarships and grants (chapter 1), education tax credits (chapters 2 and 3), and Qualified Tuition Programs, also known as 529 plans (chapter 8).
https://www.irs.gov/pub/irs-pdf/p970.pdf
After looking at all the information you have provided, here's my educated guess at a financial forensic breakdown of the 1098-T and 1099-Q forms, and what this means for tax returns that you and your daughter file.
Box 1 of the 1098-T -- this shows the payments received by the school in 2019 that the school allocated to qualified tuition and related expenses. These are expenses that are considered qualified for education tax credits (either the American Opportunity Credit or the Lifetime Learning Credit). It looks like the figure of $31,517 was derived as follows:
25,225 total tuition for fall '19 from:
18,500 -- tuition exchange scholarship (8/16/19)
2,075 -- local scholarships (8/16/19)
1,000 -- National merit scholarship (9/12/19)
1,373 -- direct loan (8/16/19)
1,193 -- 529 account (8/5/19)
1,084 -- OOP
202 total qualified fees (undergrad activity fee) for fall '19 from:
202 -- OOP
6,090 partial tuition for spring '20 from:
6,090 -- 529 (12/30/19)
2019 1098-T Box 1 = $31,517 (25,225 + 202 + 6,090)
As you can see, the school apparently applied the 12/30/19 529 payment of $6,090 to spring '20 tuition instead of that semester's room and board as you intended. Also, the only fee paid for fall '19 that the school deems to be qualified for education tax credits is the undergrad activity fee (this probably also holds true for being qualified for payment using 529 funds).
Box 5 of the 1098-T -- this shows the total of all scholarships or grants administered and processed by the school in 2019.
18,500 -- tuition exchange (8/16/19)
2,075 -- local scholarships (8/16/19)
1,000 -- National merit scholarship (9/12/19)
2019 1098-T Box 5 = $21,575 (18,500 + 2,075 + 1,000)
Education Tax Credits
To be on the conservative side based on how it looks like the school allocated all the 2019 payments, whether they were for fall semester or spring semester expenses, it appears that you have $3,131 in qualified expenses, not paid with scholarship or 529 money, that can be used to claim the American Opportunity Credit. This amount would give you a tax credit of $2,282.75, and assumes that you qualify for the credit in all other respects (read chapter 2 in Pub 970).
1,373 direct loan for fall '19 tuition + 1,084 OOP for fall '19 tuition + 202 OOP for fall '19 qualified fee + 472 OOP for fall '19 books = $3,131
Taxable Scholarships
It looks like all of the scholarship funds received in 2019 were used for qualified expenses (tuition), so none of the scholarships should be taxable. HOWEVER, for the tuition exchange scholarship, this could depend on facts that I am not aware of. Read the "Other Types of Educational Assistance" section in chapter 1 of Pub 970.
Excess 529 Distribution
It looks like all of the 529 distributions were spent on 529 qualified expenses (tuition, room and board) in a correct timeframe, so I don't know why Turbo Tax is alerting you to a penalty based on 529 distributions.
I haven't delved deeply into the spring expenses, because it looks like everything is ok for the 2019 tax year, which is what you are probably concerned about right now.
As I mentioned in an earlier post, I am not familiar with how Turbo Tax does things, so I can't provide any suggestions on how to make it work any better, other than start over, read everything very carefully, and try your best to make correct entries according to the instructions.
How the dollars from your multiple sources (OOP, loan, scholarships, 529) are allocated to specific expenses can have a huge impact. For instance, if you had used 529 money to pay for the computer instead of paying OOP, and used that OOP money for tuition, you could have maxed out the education credit at $2,500. Likewise, the school allocating your 12/30/19 529 payment to spring '20 tuition instead of spring '20 room and board might cause headaches for you down the road. The first step is to really understand how all this works, and the second step is to be proactive in planning for college expenses and payments.
Good luck.
Edited to add: DO NOT RELY ON TAX RECOMMENDATIONS OR ADVICE FROM AN UNKNOWN ONLINE SOURCE. THIS INCLUDES WHAT YOU ARE READING HERE. Always be sure that you know what you are doing and why. If you aren't comfortable, engage the services of a tax professional.
