two components, a disc and a cylinder stick. I want to strengthen the structure by adding another two oblique sticks at the base, so I copied the long stick, rotated and put into position.

Of course now I need to remove the excess parts, and that’s my problem. I tried to select the two sticks, which are components, and “intersect with selection”. I get this:

Then I tried to explode the oblique stick:

And erase the extra parts:

I’m not sure this is the best way to achive this, and it’s a lot of clicking. And, I can’t remove this blue lines or I’ll create holes in the shape:

Also if I try to erase the bottom part, the whole oblique stick disappears:

Should I explode the whole drawing? But then I won’t be able to modify the components, I loose them.

There are several issues with your model that are making it hard to edit.

One is that you have 180 segments in the round end defining the cylinders (stecco). Since the cylinder is only about 10mm in diameter, this means the rectangles defining the side surface are quite narrow (turn on view hidden geometry to see them). When you try to intersect faces, SketchUp has difficulty with the very small geometry that results. Try scaling the model up by a factor of 10 or 100 before intersecting, clean up the intersection, then scale back down afterward. Also consider carefully whether you really need so many segments in the circles. It will most likely look fine with a much smaller number.

A second problem is that you have used scaled instances of the same component (stecco again) for both the vertical and the diagonal cylinders. This means that any edit you perform on one of them also affects the other. This is pretty certain to cause confusing behavior when you try to intersect them! Make one of them unique before intersecting.

A final issue involves correct use of Intersect Faces With… This Tool always puts the resulting new Edges into whatever “editing context” is open at the time. If you just select the two sticks, the intersection Edges will go into the general model context, not into either stick. That means it won’t interact with the geometry in the stick. If you open one of the components for edit, the new Edges will go into that component. You may have to copy the intersection geometry separately into each of the two cylinders to get the results you want.

This is in fact useful if you need to keep the groups or components separate. You can select the intersection edges, copy them to the clipboard, enter the context of each group and Paste In Place. Then you can remove the intersected geometry separately, without needing to merge the groups.