PvEing in PvP gear is definitely the correct answer. PvE gear lacks the resil of pvp gear while Pvp gear has good core stats but may slack a little. Still if someone comes into a BG/arena in pve gear they will be lolfacerolled.
Not if they have a great healer in their comp. Though they should still have a minimum of PvP gear but a few DPS classes being in full Heroic raid gear and 1-4 PvP pcs will wtfrapetehhealzorz on the opposing team.
False. Season 1 of RBGs on my mage i ran with 0-400 resil (depending on my healers). Full heroic geared arcane mage. First season mmr was 2300, and then the people i played with xfered.