Our son turned 18 in 2017 and started university. He lived at home for 8 months, then at university residence weekdays, home weekends. How (or do I) claim?

There is no claim for dependent children living at home and no claim for dependent children living  in residence.  If the student has a T2202A tuition receipt and does not need to claim all of that credit he/she may transfer the first $5000 to a parent.