First time filer with questions re: May college grad with scholarship greater than tuition, new W-2, and how to file

My daughter is filing her own tax return for the first time, and we have questions re: a couple of areas.  My husband and I qualify and are claiming her as a dependent on our 2022 tax return.  She was a full time college student, living at home, graduated in May, then moved out of state for a job in late July.  She has a W-2 to enter from her new employer.  I know that she has to answer "yes" to the question "can someone else claim you as a dependent" since we can and are claiming her.  

 

Regarding education,  she has a 1098-T that shows a higher amount in Box 5 Scholarships ($7,500) than Box 1 ($4,200).  Book expenses were under $200, but were paid by us the parents.  On her tax return, does she go through the Education section and input the 1098-T amounts?  There aren't any expenses to claim since the scholarship is higher.  Or how does she enter the excess scholarship on TurboTax?

 

My husband and I use TurboTax download on a laptop to do our taxes.  Is it recommended that our daughter do the same and sign up for her own TurboTax/Intuit account?

 

Does it matter who files their taxes first...parents or daughter?