Yes, it's surely possible. Now to be honest the $1,200 worth not enough to them, if you asked them by telling there are 1000 LTC sitting in the address,They would already recover the coins.
I know that Bittrex charge a fee to users to recover coins and the minimum must be at least $5,000 :/
No it's not possible.
Cryptopia is now in liquidation which means all assets will be frozen and then the liquidator decides who gets paid back what. OP may be a long way down the list. The private keys to that wallet be not be accessible anyway, or available to a hacker.
Unforgivable that Cryptopia encouraged anyone to deposit anything. They must have known they were on their way out.