I'm a coursework MMath student myself, though I'll be converting into the thesis stream. I'm not from India, but there are definitely quite a few Indian coursework students here from. I can help answer any questions you may have.
You can probably finish in 12 months if you take 3 courses in some of your terms, although the recommended course load is 2 per term. There's been a shortage of TAs lately and so they've begun drafting coursework students to help grade some of the classes, so there will definitely be opportunity for you to land some cash there, at a pretty decent hourly rate too from what I've heard.
All of the companies from Silicon Valley that come to recruit on-campus have dedicated infrastructure for dealing with visa issues and permits, so this is more or less a solved issue for them and you don't have to worry much about arranging work authorization. If they want you as an employee, they will have you, it's pretty much as simple as that. The trick however is actually landing a Silicon Valley position without the prerequisite job experience. More on that below.
The job market is what you make of it. There are PhD and other graduate students here that struggle to land even the most basic internships, but there are others who have found success. You don't get the co-op designation until you apply for it in your second term, and it's kind of a useless designation anyway since you can always just take a leave term to work on your internship like some of the thesis students do.
There are many roles in Silicon Valley, but since you will not have access to JobMine (and none of the grad students do), it will be difficult for you to get the full information on what opportunities will be available. I've found personal success by attending info sessions to network and submit my resumes, but the onus lies on you to do the legwork and apply to companies off JobMine. But my success with internships is definitely not the norm from comparing notes with fellow coursework students (there really aren't that many of us), and you will definitely have to hustle to put yourself on the map. Most of the companies that show up on-campus are highly, highly competitive and usually bestow themselves upon upper year undergraduate students who have already been through much of the curriculum and also have a few quality internships to boot.
To be quite frank, it seems like some of the Master's students have been subject to much lower admissions standards. Some of them can't even program as well as the undergraduates, who have had to face much stiffer admissions requirements, so you kind of have to show that you bring something to the table. If you don't have a compelling resume (i.e. you don't have the ability to already land interviews with Silicon Valley companies), then I would highly recommend enrolling in one of the "Big 3" courses in order to distinguish yourself from your peers who will mostly be engaging in easier selections. You will definitely be one of the few Master's students to do so.
So basically being a Master's student here confers no direct advantages since you'll be basically applying to companies without the aid of JobMine, just like you would if you were to attend any other school.