The answer is yes to both questions.
The IRS says
that vacation and education are two of the reasons that count as temporary
absences, and a child is considered to have lived with you during times when
one or you, or both are temporarily absent.
Healthcare.gov
allows an exemption for U.S. citizens living abroad.
If you paid more than half of his living expenses, it sounds like you may claim your child without penalty for lack of health insurance.
