How much space between cables is enough?

No rule, not the same- and belief and reality, depends on who we are talking about. There's way more going on here than space. Check out my system. https://systems.audiogon.com/systems/8367 A long gradual process of trial and error going on there. Those cables are routed the way they are because it keeps them at a good distance, from each other and components, keeps them off the floor, and suspends them where they are largely free of floor-borne vibrations. 

The last picture in my system pics is a close-up of the most recent thing I have learned, that cables sound a whole lot better when suspended in free air. Having them away from each other reduces electrical interference. This is critical with phono leads, important with interconnects, somewhat important with power cords and speaker cables. Keep at least a few inches space around them, and where they must come close its better to be at right angles than parallel. 

Aside from phono leads, with line level interconnects, power cords and speaker cables the biggest improvement by far is the rubber band trick shown in my system. Elevating them off the floor is second. Interference runs a distant third. It may make more of a difference if yours are all tangled in a mess but if they are already fairly far apart then dressing them a little better won't do much. Rubber bands however, different story.

No offense to your photography skills, but I can't tell what is going on in the last picture. All I see is the cardboard "tunnels". Is the idea to have the cable supported solely by the rubber band? Like a small hammock?

Cable art, I got pretty good at it...  then BUMP it! like dominoes. Then there's one kinda tweaked, way the heck in the back of some place.

Mine looked like crop circles at the bass bins.. LOL, coiling XLRs or RCAs. My dog is an acrobat, never touches a thing, good girl.

I been thinking on MC cradle suspension, I'd need a few and rubber bands rot. Need something with a longer life, I think. I've seen clear zip ties, last 30 years, out of the sun. Beed, ladder, flat or round, zip ties might be an ART option, also... They are called Cooler ties, round stock with round cleated locks.

Regards.

Cable Elevators are ceramic insulators commonly used on telephone poles. The top has a cradle or saddle shape with the cable normally laying in the saddle. Yellow rubber bands are stretched across this saddle. The rubber band stretches and supports the cable just above the saddle. There's not a lot of space, but if you look at the earlier photos you can see the cable is resting down more in the saddle. They don't have free range to bounce like the speakers but the bands do hold the cable away from the elevator leaving it free to vibrate on its own. 

The cardboard tunnels are PPT eMats cut and shaped into tubes and painted with Taytrow TDF.