Would I be considered a full-time student if I attended high school in 2023, but graduated in June and started community college in December of 2023.

Yes, you would be a full time student in 2023 since you had at least 5 months of being a full time student.

Yes, high school counts for the full time student dependent rule.  To claim tuition credits, you college enrollment only needs to be half time or more, with no specific number of months required.