Help! What to say to my boss about my leave?

I am currently interning in a BB‘s BO and was offered an investment banking internship at a boutique bank. I wanted to ask for some advice on how to communicate with both sides and have a happy ending/starting. I am writing this email to further elaborate the details of my situation.

I was expected to start working in the boutique bank mid next week. I am currently working with a senior manager at my current firm on an internal project. I have been with my current firm since the past fall. My manager treated me very well and was happy with what I had achieved then extended an offer for this spring. It is very likely that I will be expected to work full-time after the internship. I am worried that leaving at this stage would probably prevent me from seeking future positions with the firm.

I was trying scheduling a time to report the project so that I could finish the project and quit. But my manager is very busy and the available time is uncertain. Neither firm knows about my commitment with the other bank.

Also, I have to get permission from my school in order to be eligible for an off-campus internship. In order to change my employer, I need to get a letter from your current employer stating that I will no longer be working at their company.

I was concerned about what I could expect to get from the internship. I have been speaking with the students who used to intern in the boutique bank and they told me that most of the work they did was random stuff, but they did benefit from the experience and was able to land some interviews with big banks. None of them got investment banking offer after the internship since they did not pass the interviews.

I wanted to have finance/ investment banking experience to further explore my interest in finance. I am a lower senior majoring in accounting and most of my past experience is in BO. Although a full-time offer won't be extended at the end of the internship and no much training could be expected from the investment banking internship, the responsibilities given in the position still attract me much more than the work I did in the past few months. I really want to start my career in investment banking.

My questions are:

1. How should I respond the boutique bank as for the starting date and ask for more time to proceed the documents?
2. How should I communicate with my manager and ask him for a letter stating that I will no longer be working with him given the fact that he works in another city?

I would appreciate it if you could provide some advice and insights.