I attended school in spring quarter 2021 and it was 5 credits which the school considers part-time, and then in summer quarter 2021 I attended again but 10 credits and the school considers 12 credits or more as full-time, Am I considered full time?
Each school defines "full time" in its own way. Check with your school's registrar office to be sure you are considered a full time student.
For the education credit, you only need to be half time student or more to claim the credit.
What about the earned income credit tax? Would I be considered part time on there as well?
The minimum age to claim the EIC is generally age 19; however, if you are a specified student (other than a qualified former foster youth or a qualified homeless youth), you need to be at least age 24.
Per IRS:
Specified student:
You qualify as a specified student if you were enrolled in a program that leads to a degree, certificate, or other recognized educational credential, and carried at least one-half the normal workload for your course of study during at least 5 calendar months of the year or an academic period, if longer. For purposes of determining whether you were enrolled during at least 5 calendar months, count any month during which you were enrolled for at least part of the month. The 5 months do not need to be consecutive. irs.gov