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Are there papers that sum up ideas and results from other papers? What are their characteristics/form? Do they provide insights on the field or try to predict the future?
I have read some papers for a class homework and I would like to know whether I should try to summarize and publish it somewhere.
The sum up papers you are referring to are called review articles. In order to write one, you should know the research area in question very well.
Note that there are also systematic reviews and reviews of reviews (tertiary reviews).
I second blabla's answer, short and too the point, with adequate amount of emphasis on very well :)
I'll expand it a bit by saying that journals are not typically interested in review papers that merely summarize other papers in the field. It is not simply a report on the papers you read: this has some value for your studies, but it is not a valuable publication in academic research.
The value of a review paper is to provide perspective, giving the author's deep insight into each of the papers and the way they articulate together, his ideas of the directions in that particular subfield, a critical overview of the recent advances and deadlocks still to overcome.
However, while your summary paper (or bibliography report) is probably not publishable in respectable peer-reviewed journals, it doesn't mean you cannot publish it (in the sense of “making it public”). If you are careful about how you title it (not “review paper”), you could upload it to your webpage or to arXiv.org, so that it is useful for other students discovering this field…
This is one of those questions that depend on the area.
In some cases you can do a summary or a review, e.g. a survey paper or a review paper. These papers are very useful because they provide an overview of the state of the art in some area, (if they are well written) they are good for citing and for anyone who is not yet an expert and is interested in the area (new grad students, interdisciplinary people that can benefit from an overview, etc.)
Sometimes you may prefer to do some evaluation, benchmarking or comparison, this is usual in computer science and I guess it's normal in engineering and other sciences (robustness tests, stress tests, statistical significance and that kind of things). So this takes more than listing papers, it takes executing/testing things, maybe on new settings, obtaining new results and publishing these results. The difference with research papers is that you don't develop a new system/theory, you only test them on a new (better) setting.
Finally, some people (but probably not you) can write a position paper, where they make educated guesses about how the future will or should be, the directions of research, etc. This is usually done when you are an expert and your opinion matters. Usually nobody cares about the opinion of grad students. Personally I don't care about opinions in general, but these papers are interesting because they influence decision makers and investment in research, they are self-fulfilled prophecies to some extent.
There may be other possibilities that I cannot think of now.
