So question to see if any of these work.
1- First if I place a Ranger Trap using "Expansive Trap Ability" feat, which lets the trap take up 4 squares instead of 1. Can I place a trap under the feet of an opponent, thus setting is off?
2- Kobold Snare Setter has "Deadly Traps (Ex)" which says:
"Snare setter's traps deal an additional 1d6 points of damage on the first round they're activated. This damage is of the same type the trap normally deals."
So empathizing on the "same type the trap normally deals"
How does this effect something like the:
-2a- Blightburn Trap: Increase ALL the damage types? Ones of my choice (Con Damage)?
-2b- Over-sized Barbs Trap: 1d4+1 barbs which each dealing 1 point. Extra Xd6 PER barb? Or just Xd6 to the trap overall?
-2c- Poison Trap (Su): Inflicts poison which is part of the trap, normally 1d2 per 6 rounds. Snare setter only increase the damage on the First round, but possibly 1d2+Xd6 Con damage?
3- Does a Slayer's studied target apply to Traps you set? I assume yes.
4- Can you pick up (some) of your traps? Swing them as Improved weapons? Boxing glove bear traps would be wonderfully scary.
The rules aren't clear about some of your questions.
1) Unclear, but as a GM I would rule no, you can't just place the trap under their feat.
2) Again this is unclear, but "damage" in this instance is referring to hit point damage, not ability or other types of damage that do not cause HP damage. If there are multiple different types of damage (like fire and acid) I suppose you could choose which type gets the damage boost.
3)
The DCs of slayer class abilities against that opponent increase by 1.
The DC of slayer class abilities increases. If it's not part of the slayer class, the DC doesn't increase. So unless you have a slayer archetype which grants traps, then no, it wouldn't increase the DC.
4) Unclear. The rules don't state or account for any such kind of activity so I would say no.