To answer question #1: The Ms in computational finance from Carnagie Mellon will help you become a quant. I (briefly) knew someone who did that program and he is now making boat loads of $$ at a nice company. I’m sure you can get the same result from the program at Columbia too.
I agree with Greenman. For what it is worth, CM’s program has a reputation for being more computational. You will use a lot of programming, and maybe that is good for your background. Columbia is less computational and more math focused. But in general, yes, you need to get accepted before making the choice.
For you, MFE will be better than CQF or FRM. You will get the university brand name, alumni network, and campus recruiting. This is what you need to break into a new field, not just academic knowledge.
If you haven’t done so already, I think you should pose your question on forums like Quantnet and Wilmott. They can also give you feeback on different quant programs and what they can offer. For what it’s worth, career support / networking at Columbia is not rated as highly as their academic program. Once you graduate, you’re pretty much on your own. And if you don’t already know, Wilmott is likely going to be biased on the CQF, since Wilmott himself created and runs the program with Fitch Ratings.