Thanks for your questions. Youve asked some good ones, and none of them has a single answer. That said, heres my perspective on each of them:
1. My thoughts about this question emphasize one of the things that I think is so great about engineering it is incredibly varied. My career has had many stages, and some of them have required more math than others. The last time I used a LOT of math was in graduate school, mostly in classes. Since then, my work has involved lots of work in the laboratory, lots of critical thinking and experimentation, and more recently, working with lots of people in large teams and organizations. My work has not required that I do a lot of math per se. There are engineers who do a LOT of math, either to model something such as a process or to understand a phenomenon in terms of fundamental principles. While I have not done a lot of math since graduate school, I wouldnt say that the bulk of my work has been thinking-of-ideas-related, either. Instead, my own work has been at the boundary between science and engineering, where I have spent a lot of time understanding a tiny aspect of how the world works (in my case, in materials science and engineering) so that I can then identify new materials and structures to meet a particular need. Clearly, I am thinking of ideas all the time, but then I need to evaluate those ideas to select which ones are the most interesting and most likely to pay off, and then I need to test those ideas by talking to people, doing experiments, developing models (which may involve math), etc. to see if they are valid. The fact that I dont use a lot of math every day does NOT mean that math is not valuable in my job it is. I need to be able to understand models and theories (developed by others) that affect my work, for example, by suggesting fruitful directions for my experiments. I need to be able to evaluate, at least to some degree, mathematical papers in my field so that I can determine whether or not they are relevant and, in some cases, even right. The ability to do math and think mathematically imposes discipline and logical thinking that is essential in all engineering, whether or not you are doing a lot of mathematics yourself.
2. As a general rule, it is extremely valuable to be able to express yourself clearly in both speaking and writing. It is also important to have good interpersonal skills so that you can work well in teams and, when appropriate, lead them. If you can do these things, then you will be able to clearly explain your ideas and your work, you will be a key contributor to group efforts, and people will be able to see how good your work is. You will also benefit from being able to speak up clearly so that your ideas and thoughts are heard and understood. Volunteering for tasks and assignments will give you an opportunity to show what you can do and will demonstrate your initiative, and going the extra mile to deliver outstandingly on your assignments will show that you are far from an ordinary employee. These are all things that will help you stand out from the crowd and get you recognized for what you can give to your employer. This is, in my opinion, not being a salesperson in the usual sense of the word. It is, however, the best way to sell yourself as a key, exceptional employee. I think it is what you would want to do to excel in any job, be it in engineering or in some other field.
3. There is really no one answer to this one, since not everybody finds the same things to be difficult. As you go beyond your first year of engineering, your classes will become more focused in particular areas, and you will start to have a bit more flexibility to choose the ones that are most interesting to you. They will get harder in the sense that you could not be able to do well in them without having taken the introductory classes that you are taking now. But if you are well prepared, they will likely be little, if any harder than what you are taking now. The most important points are to: (1) keep up in each of your classes, not waiting until the end to do all of the work; (2) get help from your teacher, TA, or other students early if you are having trouble in a class so that you dont get too far behind; (3) concentrate in an area of engineering that really interests you.
I hope that you find these answers helpful.