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Scope for Higher Studies after B.Sc Mathematics:
There are various options available for B.Sc Mathematics graduate to pursue their higher studies. Details of best higher studies options for B.Sc Mathematics graduates are given below.
M.Sc/Ph.D: One of the best higher studies option available for the B.Sc Mathematics graduate is to do Master's Degree in Mathematics followed by Ph.D or M.Phil. Thus, they can find a promising career in Research or Teaching field. Another option is to do Master's Degree in Economics or Econometrics. This will help them to pursue one of the best career options, Indian Economics Services (IES).
MCA: Master of Computer Application MCA is the best higher study option for the B.Sc Mathematics graduates, who wish to pursue their career in IT sector. Research Agencies like Defense Research and Development organization prefer MCA graduates with Mathematics background in their Remote Sensing Centers. So, MCA is a good higher study option for the graduates in B.Sc Mathematics.
MBA: Master of Business Administration (MBA) is the best higher study option for the B.Sc Mathematics graduates who wish to pursue their career in Management field. If they do the specialization in Finance in MBA, then they can reach up to higher positions like Chief Finance Officer in Corporate Sector.

That is really a good question.
Let start from basic, as a fresher in the industry when you pass out from college it's really important to have national experience first with a well-reputed brand Oberoi's, Taj, ITC, because there you will learn ground reality.
Yes, working abroad is more tempting, more perks, higher pays, but first of all, you must learn basic of industry and that is best learned from your country of origin.
Depends on which country you are going settle in, if their main language is English it will be easier. If they have any other foreign language as the main language, it will be a bit difficult in starting, if you don't speak their language. Without knowing the language, it will not be easy for you to handle guest, not easy operations, maybe when you are going out you can't communicate properly.
Once you are done with language and understand their culture, it will be easier. It may take 6-12 months depending on your learning capabilities. Also, the major thing is learning the domestic culture, and not to hurt anyone's sentiment when working in some other country.