What are some of the factors that help determine a good design?
Adherence to standards, repeatability and reliability, cost-effectiveness, and manufacturability are some of the top determinations of how well a product is designed.
Since Mechanical Engineering covers a broad list of topics, how does a student know which field they would want to specialize in?
Most US ABET-accredited Mechanical Engineering programs follow curriculums where manufacturing, fluid mechanics, and solid mechanics are taught. In fact, the PE exam - professional engineering qualification - recently updated their Mechanical tests to know cover (1)HVAC and Refrigeration, (2)Thermal and Fluid Systems, (3)Machine Design and Materials. As to which track a student would be most suited is up to him or her. My recommendation would be to pay attention in all these subject classes and to not dismiss any of the tracks too early. You are going to naturally see yourself excel in one of those tracks, and later the first job you get out of college, or internship, will shed more light on what area you have the most strengths.
From an engineering perspective, why are manufacturing jobs being outsourced out of the US?
Disregarding socio-economic and political factors, there are many other reasons why manufacturing jobs are shipped abroad. Although there are known process improvement methods such as Six Sigma and Lean Manufacturing, their implementation is not widespread since they're expensive and hard to implement. Another reason why jobs get shipped abroad, which I base on my internship experience, is that manufacturers usually do not take measures to conserve resources. Whereas some practices do have guidelines to reduce bottle-necking, they are usually obscurely generalistic and not stringently applied. It is a manufacturing engineering student's job to be aware of the aforementioned challenges when he or she is in college, so he or she may be ready to address these issues.