What if i use that inputs for sending the coins to another party and i pay around .001btc per kb as fee which is pretty high i guess, will it help the parent transaction to get confirmed faster?
Depends. You are effectively creating a transaction that miners who applies the CPFP patch would consider to include in their blocks. The miners would want to mine the whole tree of transaction and collect all the fees. However, not every miner applies the CPFP patch and it is currently a low percentage, I believe Eligius is largest*. It may help if Eligius considers to include yours into their block.
* Please correct me if I'm wrong.