Does your bitconnect-qt wallet need to be running 24/7 in order to get your maximum stake? OP doesnt specify
just need to put the bcc in your wallet, and wait at least 15 days before it starts staking.
You also need to leave your wallet open and running to stake, yes. You need to unlock the wallet "for staking only" and just leave it running. Doesn't use much resources at all.