I made a mistake in terms of the job title in one of my internship experiences. I put down the credit analyst intern initially since I was working in the credit department in a bank. But after researching the job description, I realised that the job I did was far from a credit analyst. I'm more like a general intern.
Correct it in the background check to a generic Credit Intern, chances are you'll be fine. But there's nothing else you can do unless asked. In which case you can make an explanation Best not to draw attention to it otherwise.
It's fairly minor at the end of the day and job titles are company specific, in this case the company itself doesn't know what the title was so are unlikely to argue differently.
I was required to put down the contact number of a manager. Is it reasonable to put down a personal mobile number in this case?
Yes, you don't have any other options.