Question – I am f- visa holder in the US have awarded

I am f-1 visa holder in the US; have awarded international students scholarship. I completed the first year of my two years graduate program. I was working as a teaching assistant in the University in last spring 2018. Now I’m doing my summer internship with CPT (Curriculum Practical Training). And, I just get married this month and I am thinking to file for adjustment of status. My questions are:
a. The I-485 form asks for employment history so do the on-campus teaching assistance and internship considered as employment?
b. If I file for adjustment of status now Can I continue working on the internship with the CPT?

Question – A student is current

A student is currently working on CPT which ends today. Their OPT does not start until July. Are they able to continue working as an unpaid intern/volunteer until their OPT becomes active?