It depends how many Google services you use but it could be a lot. This could be your mail, your docs, calendar, messenger, voice, etc... Plus other services that use Google auth.

This request seems very improper for them to request that you set a password the same as their personal email. This actually violates security best practices. I would be very suspicious of why they are requesting this. Also that they specifically state that the registration process may encounter errors and to keep doing it is also suspicious. Are you sure this is a legitimate request? It appears to me a phishing attempt to me.

If this is legitimate, this company and your University need to be named so others can avoid these kind of bad practices.