Public dataset without license: what is allowed?
This may vary by country, but in the US at least, the default terms (if no alternative is specified) are "all rights reserved", which means that you are not allowed to reproduce the work (the dataset), prepare derivative works from it, sell/rent/lease it, or publicly perform or display it. In particular, redistributing it to others is not allowed. In practice, the authors may be fine with it, but legally speaking, you're not allowed to redistribute the dataset in the form it was published in, without having explicit permission (which could be provided by a Creative Commons license, for example).

If you wanted to reproduce the dataset in a different form that conveys the same information, that may or may not be allowed. It would be up to a court to decide whether that counts as a derivative work or just a use of the underlying ideas, and a copyright lawyer could advise you better on whether your desired use is legally acceptable.

You are allowed to read the published dataset and use the ideas contained within it (i.e. the data) to draw conclusions. Copyright law does not allow for the restriction of those rights. I think doing an analysis on the data and publishing the results of that analysis (but not the data itself), as you would do in the process of writing a paper, is generally considered to be fine.