Yeah, I can't really tell what the issue is with the skybox from that shot either.
World details will render in front of skybox IF they are in a visible leaf.
Probably what happens is from that view you can see into the leaf, so they are there. But when you move you move into a new leaf that can't see the leaf they are in, thus the disappearing act.
Instead of having a square corner maybe have a 45 degree angle. Or expand the height/width/whatever of those areas so the leaf issue doesn't happen.
The skybox DOESN'T have to be really tight to the gameplay area. You can have world area the player just can't get to due to walls/fences/player clip. Have some extra room behind it, then have skybox.
Hard to tell also, but it looks like your skybox might be too low, make sure you have enough room for a demo to get at least a 'one sticky' jump in without hitting his head.
Demos can go so high with 2 stickies I don't generally plan around that, just too hard to optmizie your map AND let demos have full jump height. But it sucks to hit your head when only using one sticky.
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And I think something is wrong with your hud, I've never seen that before
