How do I write a career mission statement? Why do individuals need goals? Why is it important to write goals down? What is self-talk? What effect can negative self-talk have on your career? What is the difference between smart and stretch goals? What are the elements of career management?

As there seem to be several different and not entirely related questions here, this answer will focus on giving you a starting point for answering some of them.
For the mission statement, you should think through the big picture rather than focusing on narrow immediate goals. In other words, you should think about whether, for example, certain forms of corporate social responsibility matter to you or whether you are focused purely on financial success. You should also consider what you would consider a major life achievement; for example, would you be most satisfied with innovating technologically, improving people's lives, or building a company as an entrepreneur?
This relates to the difference between SMART and stretch goals. SMART is an acronym for "specific, measurable, achievable, realistic, timeline." These are narrow, short-term goals that are steps on your way to "stretch" goals, which are your ultimate aims. In a sense, stretch goals are where you aim to end up, and SMART goals are checkpoints on the path. Your mission statement reflects your ultimate stretch goal. 
The point of developing these goals is that clearly written goals are the keys to success. You can use them as the basis for making a variety of career choices. For example, if you have a choice of two job offers, or even choices of various electives in your degree program, you can ask yourself how they contribute to your goals. For example, if your eventual goal is to be an entrepreneur, you might want to develop knowledge of management and finances, while in marketing you might want to focus on PR, marketing, communications, and media courses.