Not just the site and content, I want to locally reproduce script calls, etc. I tried HTTracker and wget but it doesn't work.
As an example take donjon.bin.sh
There is no way of using HTTP to download a whole website if some portion of it is non-static such as that produced by server-side scripts or programs.
Normally you would need an administrative user account and would typically use a different protocol such as FTP to transfer the site. In addition you would need some means of extracting the contents of any databases used.
You will have issues if you're trying to download web servers that are not 100% client side scripting. If the site uses any sort of server side scripting (ruby, python, php, asp, etc.) then you would only be able to download what was rendered and not the actual source files that generated the client side content.
The search terms that you may want to research is web crawling. For example, Google uses a crawler to cache data from websites. A lot of times if a website disappears or is shutdown, you're able to look at the Google Cache of the last time it had data. Useful for some older content sites that are no longer in existence.