Background Check for unpaid part-time internship experience

I got an offer from a BB and am currently undergoing a background check. I was not a typical finanical background for my undergraduate so I did not get a summer internship after finishing my undergraduate. during that summer, I did an academic research with one of my professor from school and also an unpaid PTA job at a well-know company outside the states. Part of the PTA work was done onsite and later I moved back to the states so the remaining work was done remotely. However, in my resume, I did not distinguish this unpaid Part-time assistant experience from other professional experiences and the location was rephrased as outside the states for the entire duration. I did not go through HR process for this PTA but I have a reference letter/recommendation letter from my supervisor.

In the online form of the third background check vendor, I did not include this experience in my employment section. Would that cause any problem?

Another thing I was worried about is that during my undergraduate I transferred from a small liberal art college to a target school on my junior year, but I did not include this school information in my resume. Would that be an issue?