1. Does any mining pool allow the miners to add their own transactions to the block ? If so, who ?
Most pools supply the hashers with block headers that are ready to be hashed. So, in most cases you would not be able to add any transactions to the block that you are hashing.
Some pools might (as a benefit to their hashers) allow hashers to request that a transaction be included in the next block. That's up to the pool operator to decide if they want to provide that as a service or not.
It is also possible for a pool to allow the hashers to build the blocks themselves. Most pools don't do this, because most hashers are lazy and don't want to get involved in that part of mining.
I believe P2Pool allows the miners to build their own blocks, and F2Pool allows a couple of their participants to choose transactions for the blocks.
2. If this is not possible then is there any other way for the transaction to be confirmed sooner by a miner other than including higher fees?
Miners are spending a lot of money on hash power. Most of them are doing that with an expectation that they will earn revenue that is higher than their costs. The higher the revenue, the more profit they make. That means that including a lower fee transaction will reduce their profit. As such, your choices would be to either pay a mining pool directly and ask them to include your transaction, or wait for a pool to confirm your cheap transaction out of the charity in their heart.