When intersecting faces of two components, the intersection fails unless I explode the component I’m trying to intersect with the model. After exploding, the program does produce the intersection but deletes several faces thus making the model unusable. Any suggestions?
Not sure what is your goal, but if you delete some entities from the horizontal “rod”, then you will get solids so you can use solid tools, e.g. split:
Did you scale up the model before sharing it here? My first thought was that it must be a small edges problem, which is what your image shows. But the model you shared is large enough that I didn’t have that problem either using “Intersect faces with…” or the solid tools (which do require removing your centering marks to get solids, as @dezmo suggested).
Even without cleaning up the solids, there is no need to explode anything! Just open whichever of the components you want to receive the intersection edges, select all, right-click and select “Intersect faces with model”.
On another note, I would recommend working in perspective projection, not parallel, while modeling in 3D. There are various graphics issues that can arise because parallel projection provides no sense of how far the camera is from the model.