You can run low voltage together (speaker wires, ethernet, etc.), no problems. Try to keep LV away from AC wiring - if you have to cross them, do so at right angles. Not sure of any specific distance recommendation.
Crossing posts less problem than running in parallel, for that, you should keep 12" apart at minimum. Insulation does not do anything unless you mean wire shielding. HDMI cable is shielded, so it should be fine. I run a lot of low voltage wires parallel to electrical wires, but I run them on the other side of steel I-Beam so the I-Beam acts as a shield. Sometime you are just not able to avoid things like this, just do the best you can do and not to lose sleep about it. If you have to cross and are not comfortable with that, you can run your speaker wire through like a 12" long short metal tube at crossing and then you should be fine. A lot of digital cable are shielded, and even they are not, they are more tolerant to electrical interference than analog cables. That being said, the shorter the wave length of the signals, the easier being interfered.
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