Where will payments and scholarships/grants show up if they were paid in 2019 but were for a 2018 semester?

Keep a copy of your student account statement with your tax file. 

If part of your grants were paid in 20159, but were for expenses of 2018, reduce the expenses for 2018. Adjust next year as needed.

According to the IRS:

Refunds received after 2018 but before your in-come tax return is filed. If anyone receives a refund after 2018 of qualified education expenses paid on behalf of a student in 2018 and the refund is paid before you file an income tax return for 2018, the amount of qualified education expenses for 2018 is reduced by the amount of the refund.

“Credit recapture. If any tax-free educational assistance for the qualified education expenses paid in 2018 or any refund of your qualified education expenses paid in 2018 is received after you file your 2018 income tax return, you must recapture (repay) any excess credit. You do this by refiguring the amount of your adjusted qualified education expenses for 2018 by reducing the expenses by the amount of the refund or tax-free educational assistance. You then refigure your education credit(s) for 2018 and figure the amount by which your 2018 tax liability would have increased if you had claimed the refigured credit(s). Include that amount as an additional tax for the year the refund or tax-free assistance was received.”

CLICK HERE for IRS Pub 970 Tax Benefits for Education