You are of course welcome to do your problem sets by hand or on a computer. But if you are going to do the latter, then I would strongly recommend that you not use a traditional "word processor" to do so. They are simply not optimized for mathematics, and their output is awful. A much better option is LaTeX, and if you want to use LaTeX in an environment that feels a lot like a word processor, then you can use LyX. Especially if you have any intention of ever doing serious technical writing, you should start using LaTeX sooner rather than later. In the sciences, especially, it is the standard tool. Many scientific journals do not accept submissions in any other form.
Problem sets will be marked on a scale of 1--5, with half points where appropriate. A 4.0 signifies a problem set that meets expectations. That is, it displays a perfectly adequate understanding of the material covered. A 4.5 signifies something beyond that: Problems that were done especially well, for example. A 5.0 is rare and signifies a problem set that displays an especially deep understanding of the material.
Scores below 4.0 signify some inadequacy in the understanding displayed. A 3.5 probably means a few too many mistakes, but nothing to be overly concerned about. A 3.0 means that the understanding of the material displayed is barely adequate. Scores below 3.0 signify increasing difficulties. Since, as with any math class, the material is cumulative, it is recommended that anyone receiving a 3.0 or lower score see the instructor to make sure the student's difficulties are addressed.