Not possible, we know that every transaction have allocated fee. Hopefully in  the future one company related in blockchain create a free transaction fee. But I think this will not happen, paying fee is going to who create the system.

There is no wallet without transaction fees. I think you'll still get a fee to guarantee all your privacy safely.

Also, transaction fees aren’t decided by the wallet. It’s decided by the network, by a whole lot of factors. It’s also optional, meaning you can choose to not pay a fee and run the risk of no miners wanting to put your transaction on a block because they won’t benefit from it.

For now there is no single Bitcoin transaction market that every transaction is free, at least there is a shipping gas cut, depending on the market rules itself in deduction,
so for those of you who want to transact Bitcoin you can choose a cheaper market in the transaction is up to you, many can be handled, I don't mention the market, you can search on Google. Or service forum: https://bitcointalk.org/index.php?board=52.0