NIE Card & Insurance (Madrid)

All,
I am moving to Madrid in March for language and master study. I was told by the agent here that to apply for a NIE card (Non-EU students), I need to register for a course longer than Protected content . With that, I will get a one-month student VISA here and only then I am eligible to apply for NIE card. if the course is shorter than Protected content , I can't extend my VISA within Spain even though I enroll the master which is a program over a year. I have to fly out to my home country and re-apply for a student VISA. Has anyone experienced something similar? it would be so much helpful if anyone can give me some insights.

As far as the insurance, which one has better coverage for non-EU students? Should I get an EU insurance or a private one like MAPFRE or AIG. If the private, which package has better coverage? I am considering to have my dental taken care of in Spain....

With many thanks - Claire!