Destroyers are tac hunters in the game's scissor/paper/stone.
They are less prone to being useless against all the other classes than said other classes.
They have the best all-around main weapons (power, clip, range, projectile speed, accuracy all above average).
Their nemesis are the dreads (you never can win in a fair fight).
You've got actually one of the only ships that can make an arty go in cover (same max range) - others being other artys and the medium dread.
If the arty could hit you three times, you were not on top of it (Blink out of its fire cone, and especially higher, and it can't target you) except if it was an oberon arty, which can't tree-shot you but is more of a skirmisher.
Were the shots red ? You may have encountered a rare build that doesn't play well, the oberon siege arty.
About playing arty yourself - were you actually in range ?
You can't steal a kill without doing more damage than the other player, so, in short, you can't steal a kill. You've done your part if it's yours.
As far as i've seen there is no damage bonus to missiles for diverting energy to weapons.
It just boosts the main weapons (rate of fire mainly). I'm not even sure there's a boost with artys (because they reload).