Skewed 3D visualization of E/Z in alkenes

[nomadreid]

TL;DR Summary

In the main text is shown diagrams illustrating the concept of together (Z) and opposite (E) sides of a double bond for substituents. But my 3D perception of them do not match up with the correct alignment, so I am obviously looking at them wrong. I also have an easier question about numbering of alkenes.

(Edit: Forgot tags; couldn't go back and re-insert. So, tag: stereochemistry.)
The following 3D visualizations are taken from
https://pubchem.ncbi.nlm.nih.gov/compound/4Z_-5_6-dichloro-1_4-hexadiene#section=3D-Conformer

For (4Z)-5,6-dichloro-1,4-hexadiene

So I am not sure how to correctly visualize these to distinguish Z and E.

Another example:
First, a side question: in
https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Organic_Chemistry_(Morsch_et_al.)/07:_Alkenes-_Structure_and_Reactivity/7.04:_Naming_Alkenes
it is stated
"Start numbering from the end of the parent chain which gives the lowest possible number to the double bond".

But what if there are two double bonds, and starting at one gives the same numbering as starting with the other? For example,
for (1E)-1-chloro-1,5-hexadiene? Here it seems that we are starting from the red, not the purple?

Now returning to the Z/E question, if we are talking about the red part, then the two bonds appear perpendicular -- so this would be neither Z nor E, but it was decided that it is E. Are the angles simply poorly represented in the diagrams?

Finally, I originally had a question about (1E,4Z)-1,5-dichloro-1,4-hexadiene, because in Example
in
https://chem.libretexts.org/Courses/Sonoma_State_University/SSU_Chem_335A/Material_Since_Exam_3_for_the_Final/Unit_7:_Alkenes:_Structure_and_Reactivity/7.05_Alkene_Stereochemistry_and_the_E,_Z_Designation
there is no 3D structure, nor could I find one on the Internet, just the

Trying to assemble a 3D structure for this, the E and Z appear to me to be reversed to the correct alignment. So my visualization is missing some key element.

Any help would be greatly appreciated.

 

[Borek]

Can you assign priorities of substituents of the "left" and "right" side of the double bond? Which has a higher priority - L1, or L2? What about R1 and R2? Z means either L1, R1 or L2, R2 are of higher priorities in each respective pair. Is that so?

 

[nomadreid]

Thank you very much, Borek. Your drawings are very helpful, and a bit of the fog is starting to lift. Let me see if I have this straight. The idea is to look at the two carbon atoms on each side of a double bond, one regards the group with the highest priority on one side, and then the group with the highest priority on the other side, and one compares them to differentiate Z or E. So far, so good; so I was comparing the wrong things. Super! I will work on this some more and be back if I still have difficulties, but this was a big boost.