I am being asked if this is my first year of school at a college or eligible school as of January 1, 2018. Is that asking if 2018 was my first semester or full year?

The reason the TurboTax program asks if this was the student's first year as of January 1, 2021 is because if it was not, the program will ask if the American Opportunity Tax Credit (AOTC) had been taken in any prior year, and if so, how many times. 

If the answer is "Yes" this was the student's first year, the program knows that the AOTC has not been used yet. 

If you answer "No" the program will go on to ask if the AOTC or Hope Credit (which was from years ago) was used and how many times. This all has to do with the program making sure the credits are not used more than allowed. It would not cause an "error" to select "No" rather than "Yes', but you would be subject to those additional questions about previous usage of the credit.

For the student that started in the Fall of 2021, you could choose either answer, since we know he/you could not have claimed the AOTC for expenses relating to "non-degree seeking" classes. 

As far as the credits for the expenses/time the students were dual enrolled, the payments would need to have been made to the college and the purpose would need to have been part of the requirements of a degree or to improve job skills. 

According to the IRS:

"For purposes of the lifetime learning credit, qualified education expenses are tuition and certain related expenses required for enrollment in a course at an eligible educational institution. The course must be either part of a postsecondary degree program or taken by the student to acquire or improve job skills."

To be eligible to claim the American opportunity credit or lifetime learning credit, the law requires a taxpayer (or a dependent) to have received Form 1098-T, Tuition Statement, from an eligible educational institution, whether domestic or foreign."

Also, I might suggest that if you anticipate the students may have more than 4 calendar years of school expenses of postsecondary education, you look over IRS Pub 970. The AOTC is usually worth more than the Lifetime Learning credit, but not always! Don't waste a year on the AOTC if the Lifetime Learning Credit has the same result. The AOTC is usually best used for the years you have the highest amount of expenses, but at the same time, once the student achieves the degree, the AOTC is no longer an option. The AOTC MAY be used for the year the student DOES earn the degree as long as the student is "at least half time" for that year as well. 

Expenses paid in the tax year for that tax year and/or the first three months of the following year count. 

IRS Pub 970