Can I publish a sum up paper? 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).