LGODream,
Thanks for your post. These are interesting questions.
Regarding the quantitative rigor of the program, I would say that it is exactly what you would expect from a graduate-level engineering curriculum at MIT, i.e. it's very quantitative. The instructors assume that you already have a full undergraduate engineering education, and they start building from there. Given your background, though, I wouldn't worry a tremendous amount about not being able to manage the quant. expectations.
If you did want to brush up on some basics before matriculating, I would recommend revisiting probability/statistics and basic calculus.
There are a lot of people who have shop floor experience. In fact, I'd say the majority of my class has worked on a shop floor in a supervisory/managerial role at some point in their career. That's definitely not a detractor to your application. In fact, those are the types of experiences that can be used for inspiration in your essays to really convey your interest in operations management.
On the subject of internship selection, I believe the process is pretty formal. I say "believe" only because I haven't actually gone through it yet. However, what I believe happens is that the partner companies offering internships will come to MIT and conduct individual interviews with each LGO who is interested in their internship offerings. Once the interviewing is completed, the partners rank their preferences of LGOs, the LGOs rank their preferences for internships, and a matching algorithm takes over.
Lastly, there are 5 international students in the class of 2013, and I believe this number is pretty typical for the incoming class (~10%). If you have permanent authorization to work in the US, definitely make mention of that on your application, as preference is given to applicants not in need of corporate sponsorship.
Hope that helps!
Bob