You know, from your description I would probably be easily frustrated with your class as well if I was taking it (I’m not very talented in the mechanical engineering department)! I struggled through my calculus, physics, and chemistry courses when I was first getting into engineering. What I can promise you is that it does eventually get easier if you stick with it! Just remember that rewarding feeling you get when you solve the problems – that happiness will never go away!
Engineering is a good career choice for anyone who wants to learn how to solve problems. Our engineering courses often force us to think outside of our traditional method of problem solving and find new answers to problems when the ones that seem the most logical don’t work. But remember, you’re not alone. Engineering is hard, that is one of the reasons why it is such a highly regarded profession. The great thing about engineering, however, is that there are so many different types.
Engineering jobs are far from scarce in our current economy. Engineers will always be needed. I caution you though against pursuing a career in engineering simply because there is a high demand for it.
The amount of teamwork involved depends entirely on the job and type of engineering you do. For example, as a human centered design engineer I work with a team of others like me. However, I have a friend who is a computer science engineer who does not have as much teamwork as I do (there are also computer science engineers who have lots of teamwork). While it’s best to know your stuff on your own, it is likely you will have a lot of teamwork in any engineering field.
Engineers design many things. I design mobile and web applications and websites, everything from the layout of the content to the visual design and overall experience. Aerospace and Mechanical engineers may design parts for airplanes. Bioengineers may design mechanical body parts for amputees (they design many other things as well). Materials science engineers may design new materials for sports equipment or solar panels. I would suggest that you start researching the various fields of engineering and that will help you find out what they design.
To your last question, again, engineering teaches you how to solve problems. It works as a base for other jobs (such as becoming a lawyer) because it gives you a way of thinking about things differently. Your ability to problem solve will never go away and can only help you in any future career.