I was recently extended a contingent internship offer by a very big company. However, in order to be officially hired, I have to pass many checks including a background investigation.

Can someone tell me exactly what goes on in the reference check process for a big company?

Also, I am worried because of the following issues:
1. I don't remember exactly from my application, but the exact start/end dates I put down for my previous internship might be a little off because I couldn't remember.
2. For my past internship A, I worked with many people in the department and I didn't have a specific supervisor, so no single manager there knows all the work I did. But I don't want to give out everyone's contact information because I think that's excessive, and even then they might not recall all the work I did.
3. For my past internship B, I worked mainly with the supervisor's assistants. Although I know that I did a lot for the supervisor, I don't think he remembers just because I didn't have that much contact with him. And the assistants I worked with all left that company B.
4. During my interview with the big company, I told them that I did a lot of work for both internships A and B, and I also told them that I made important contributions/found mistakes that could've had serious impacts. However, what I said was very subjective because I wasn't my past supervisors, and although they were true, I don't know if my past supervisors would verify just because they might not remember everything I did, and they might not see the things I did to have as profound of an impact.

Based on what I described above, would I be in trouble for the reference check? What should I do?

Thanks!