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).
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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.
Leave pvp worlds and go to a normal world, then in around 20-30 Minutes you should lose your skull (Try not to die within that 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.
Answer: You don't bring armor with you into Dungeoneering so therefore you don't lose it. Good luck! Answer: However, you can have items you pick up or create within the dungeons. Those items, you don't lose when you die.
No. But if you go into the lose all your items portal than yes.