Well, I've never run a dungeon-oriented game in Savage Worlds, but my Firefly gamers ran into a booby trap in an illegal asteroid mine once, so...it was in fact a trap in a dark tunnel!
Here are my answers to your questions:
Yes, they get a Notice roll. There
are plenty of passive tests in RPGs -
rolls to notice, rolls to resist
poisons / toxins, etc..
Just decide how hard it is to spot and set your TN accordingly. Is the trap improvised or cunningly crafted? Is it hidden by piling up some trash or by being made to look exactly like the dungeon floor? Here are some examples of how I might set TNs:
- A bear trap with some leaves tossed on it: 4
- A pressure plate beneath a flagstone: 8
- An improvised trap consisting of a vat of acid balanced atop a slightly-open door: 6
Probably. If they're searching for traps because they succeeded at some test or figured out some clue and you want to reward their previous success. I'd give a +2 bonus, or +4 if they were operating in total paranoia mode: "OK, we've constructed our trap-tripper wagon. Now who wants to push it?" Don't forget to make their movement slow for the low bonus and super slow for the high bonus. And put time pressure on them! "Alright. You've made your way safely into the dungeon over 100 feet. You're not sure when the flood will drown the princess you're here to rescue, though..."
I don't remember the details of Danger Sense. I thought it was a roll to Notice at a penalty to surprise attacks or something. I would say that an untriggered trap poses no danger. Neither does a trap that another character trips. So if a trap goes unnoticed and is tripped by the PC with Danger Sense, I'd allow a roll. If noticed, that allows another roll to try to avoid or minimize the damage. If the trap was triggered by another PC and wouldn't hurt the PC with Danger Sense, I wouldn't allow a roll. Spidey-sense doesn't tell you when anyone is in danger!
As for rolls to avoid or minimize damage in other circumstances - it depends on the trap! The Indiana-Jones-style-rolling-boulder trap is all about initiating a series of rolls where the party races the rock! But a bear trap? Poison on a doorknob? Just use your judgement.
Also - this doesn't just apply to Savage Worlds. I would say some of these pointers apply to traps in whatever system you might choose.