I've recently got interested in programming dapps on Ethereum and first question was if it is possible to place a transaction with 0 gwei or 0.1 (as I can see 0 is not possible in MetaMask) and just run special miner that will mine your transaction (or a special contract) only. I've tried to look it up on internet and I see many talks on reddit about "channeled" transactions but I never see that it actually went anywhere or someone came and said that it is impossible. Thanks!
If you're running on the main blockchain, it's possible, but not likely. You can write your own miner that uses whatever criteria you want to decide which transactions to process. Your mined block still needs to become part of the consensus, though, which makes the chances of success much lower (unless you build your own powerful farm of mining rigs).
The alternative is to use a private network. If you run your own private blockchain, you can process transactions for free.