Is it illegal to make a research about illegal stuff?”
It’s perfectly okay to visit any site where the content itself isn’t illegal. In this case, it is fine. Child porn, for instance, is another story. The only way you would be committing a crime is if you used the information you learned to actually commit a crime. About them tracing you: Yes it’s possible. Nothing you do on the internet is ever completely anonymous. Law enforcement can nearly always track down the computer you used to do something, just takes them some time. BUT they would have no reason to find you just for visiting a website.
Yes, without a permit, it is illegal to perform illegal acts, even for ‘research’ purposes. There is thin line between reading about illegal stuff (like visiting a site about hacking), or committing an illegal act (like visiting a site with child porn) The difference is, that a hacking site in itself is not illegal, as long as it describes ways to hacking etc. A child porn site IS illegal. As soon as you have a picture on your monitor that shows child porn, you are doing something illegal, and you might get a lawsuit. Again: the difference is whether the site DESCRIBES illegal acts, or whether the site CONTAINS illegal material. Oh, there are exceptions to this: as far as I know US law, it is illegal to gather bomb-making or nuclear information at all, so you should avoid those sites too. And yes, if you visit a site, they can track you down, unless you take a lot of measurements to surf anonymously.
