Is there a mod to remove the many useless research-topics in the tech-tree?
or at least one that would cut the research-time of thees topics to a minimum?

Don't think one does exist, but could be made. But I would like to know what do you consider "useless" research.

Well, all the "research this to make gun-xyz usable"-things. You can use any weapon in the game without thees, so they are useless.

Ah, those, they might have bad side effects tho. Some people have had problems when trying to manufacture something like weapon add-ons when they went straight to researching the blueprints without having researched the handling. I'm not absolutely certain about this.