Ok. Before you embark on this road it may be good to know that there is a fundamental world view difference between graphic software users and CAD users.
- CAD users think that the line is the base primitive
- Graphic software users think that the face is the base primitive
Often users on both camps lack the understanding that you can in fact use both in both cases and that ultimately it depends on you level of abstraction as to which you will choose. This reflects in the tools you see. Now unfortunately to you the simpler the software gets the less likely it is to understand this, and force the world view. In your case even worse. In 2d graphics land trim is a really advanced feature almost unheard of.*
Now the equivalent of trim in illustrator is shape builder. It is however primed to make faces by default. That's what most users are doing after all. But face priority becomes a boon when you realize you can color the areas between lines, in which case they need to be faces anyway.**
Image 1: How a illustrator user would approach your first image.
Now, I have created faces because I may want to color the surfaces later (see image 2). Though that may be a white lie, its easier to make faces than delete just lines, id have to click around and dragging lines is faster in this case. Unfortunately you may need to learn your workflow from scratch. It is painful to understand that what you take for granted isn't so self evident. Or just do it in autocad extort to PDF and open in illustrator if you feel learning something is beneath you.
Image 2: After filling image 2
** Further there is a general BUG in all, but some very special experimental, vector graphics drawing engines. So users tend to avoid making perfectly fitting interlocking shapes becasue you can see trough the corners. See this so it is natural for 2D graphics people to steer clear of this problem.