I don't have a definitive answer to your question, but in the absence of any other replies, here's a few miscellaneous thoughts: IIRC there should be a minimum of 18" separation between power lines and analog cables (like speaker wires) + for high-speed network cables you need to be >12" from mains wiring. What I'm unsure about is that as the HDMI is digital. does this make a difference? - I guess that interference could/would manifest itself as sparkles and/or maybe loss of sync. I'd try to attain maximum separation from power lines and try to avoid parallel runs if the gap gets tight - if you do need to cross over a 110v cable, do it at right angles.
The telephone wiring isn't really a problem - it's typically a spikey signal but is at a low voltage. Proximity to the air ducting isn't a concern at all.