Answer: You don't bring armor with you into Dungeoneering so therefore you don't lose it.
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Answer: However, you can have items you pick up or create within the dungeons. Those items, you don't lose when you die.
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If your in a Bounty hunter world +1 you lose everything but the most valuable item you keep. But if you die in a normal world with a skull you lose everything, but you can get your stuff back if you get to your grave in time.
The grave in RuneScape serves as a safety net. So when the a players character dies they can return to their grave and reclaim all their armor meaning full void will be intact.
While on RuneScape PVP worlds, if you die, you only lose the items you are carrying, not those in your bank, never in RuneScape will a death directly affect your banked items.
Yes, of couse(except the safe zones) You lose all your items. You should not take very expensive stuff into PVP. Or into the Wilderness, for that matter, but in PVP you get "skulled" and keep zero items instead of three (or - I believe - one item instead of four, with the appropriate prayer).
it depends on who you are battling with