Octo necklage

Does the octo necklage have to be removable in case of entanglement with something (I can't imagine how, but neither I would've imagined a suicide clip clipping to a cave line).

I made one with two double fisherman knots (four knots in total), one to grab the octo and another in the opposite side, to adjust the length. I've seen one on sale with a double fisherman to hold the octo and some other kind of knot in the back that I'm not sure if it only served for adjustement or also as an emergency release.

As long as the regulator can be pulled out of its loop, I don't see why the necklace itself would have be be removable. I would't want the regulator permanently secured to the necklace, as when the ends of the bungee are held under the zip tie holding the mouthpiece in place.

Yes, the octo should be removable from the necklace. Commercially available products are suppled by DiveRite, Manta, and Highland and probably a number of other sources. One possible situation where ability to remove the octo is important would be a small boat without dive ladder - it becomes necessary to take off back pack in the water. If seas are rough you can remove octo and wing/plate while continuing to breath from the long hose.

Does not have to be. If you do get entangled in the very rare chance you have your cutting device. If you do get entangled in your bungee backup then you're cruising too close and/or lack spacial awareness.

You should either have it ziptied to the mouthpiece (2 overhand knots) or set like the way you have it (but with only 2 fisherman knots).

The way you have it set up is a bit more complicated than what is usual. Adjust the length to the right size and then tie the fisherman knots just for the mouthpiece.
I see nothing wrong with your current way though, apart from having a variable necklace length each time you set up.

Edit:
In rebuttal to having the necklace being easily removable. For boat dives you can easily slip the necklace over your head, even with a snorkel on. True it is easier to just pop it off the necklace.
But on the other hand the reason why some divers choose to "permanently" secure their necklace via ziptie is because of the mindset that you do NOT EVER want to lose your backup. With a slip on necklace you have the possibility to lose your backup and the only way to recover is to perform an overhand back-reach reg recover.

One example someone gave me that made my decision to ziptie my necklace is if you ever get knocked over in a surf zone and become turtled. At that moment if you can't find your primary, you better hope your backup is still in it's place. If you have doubles on, your backup is pretty much your only escape until someone comes to help you.

I think I do my necklace the way you describe -- two fisherman's knots, to make a loop into which the mouthpiece is inserted. In six years of diving, I've had my reg pulled out of the necklace a few times, usually when I take my gear off in the water without remembering to take the necklace off over my head (and I'm actually quite HAPPY it pulls out then) or when gear is being moved around on a boat or in the car and the necklace catches on something. I have never had it pull out during the process of a dive, even when the unfriendly California surf has done the washing-machine thing with me.

There was a recent technical diving fatality where a 'non-detachable' necklace was likely (no survivors to confirm) a highly contributory factor.

If/when the details are released publicly, I'll confirm the details.

From that event, I don't...won't... perma-attach regs to the necklace any more (before I thought it was a non-issue).