Right now Traps&Doors skill is ridiculously weak and useless
You've never had a good character killed by an unexpected Zot trap, have you?
There's a reason the divinations school was removed. There's a reason we lost rods of divination. There's a reason Ash is so popular. The ability to detect threats, especially traps, is incredibly powerful. Training traps and doors is essential for pretty much every character. Sure, you don't want to take take it all the way to level 27, but that's true for lots of skills. You prioritize.
Piling more abilities into an already important skill will only make it more critical- especially since some of what you're suggesting has tactical applications. This will just make training t&ds more of a no brainer, and increase the penalties for builds that are slow to get it going.
Comments on your individual points:
1) I see variable LOS based on a skill being a nightmare. Ranged attackers and casters will be ridiculously penalized until they get it trained up. Stabbers and mele fighters will do everything they can to keep it low, and stumble into every trap as a consequence (I wouldn't call that an 'interesting' choice, myself). Also, train LOS too high, and you've exposing yourself to considerable danger in areas where things can smite (will make Tomb and Zigs way worse). Not to mention possible display size problems on small monitors if LOS gets much bigger than it is now. No matter how you slice it, I see it being a nuisance that will require micromanaging.
2) LOS for players / monsters is shared. If you can see them through the cloud, they can see you too. Again, this will encourage micromaging, with some people trying to keep the skill low so they can still use smokescreens effectively. I really don't like anything that penalizes players for training a skill.
3) There are already lots of ways to deal with invisible threats.
4) At high levels, this would trivialize one of the most dangerous status effects in the game, and remove interesting choices you're supposed to make to protect yourself.
5) ...isn't this what Ash is for?
6) Seems too powerful to me. Getting stair ambushed is just one of those risks you have to take. Although, if I remember right, this was recently improved by forcing you to get in the first turn when you come down the stairs- ie, you won't die before getting a chance to try
something, even if you'll get killed immediately after (someone say something if we never implemented this change).