I have many ~0.01 BTC Tx sitting on an address. All of them are unconfirmed right now. If I forward my total balance of this address to another address in one Tx and provide 0.004 BTC Tx fee, then will I be able to get them confirmed ?
No, unless the miner supports Child-Pays-For-Parent. There are very few miners that support this, so it won't work. However, you could try and hope that Eligius, one of the pools that supports CPFP, mines the block that confirms all of those transactions. Also, if you try it, put more fees on it than you calculate the minimum to be. The higher the more likely it gets confirmed.I would like CPFP to be a common rule for miners and pools. I know it will take more time to scan all potential CPFP transactions, but the process need not be a exhaustive scan. Miners could only scan the inputs of the few 1k or below transactions with abnormally high fees (example 0.0003btc or above). The will also help to single out real transactions from spam.
Probably the nodes, that mining pools are communicating with to get mempool data can be configured in a way, so that the Tx chain, which has a big Tx fee at the end will be shown above*. This way, miners will not lose any time in sorting the mempool to find out CPFP Tx chain.
*expert citation needed.
