So I am currently running a full node, as well as a GPU miner. I am curious first of all where do DApps get run? They wouldn't make sense to run on a GPU as they aren't very parallizable, so I am assuming by a full node. But I never noticed any income being generated by my full node. Where does all the Ether go that is used in Gas to run a DApp? Someone must be running them, and I presume they would get the gas a reward?
Decentralized apps can be hosted on webspaces or on github or on local machines and nobody really gets rewarded for them. I think you are mistaking the term with smart contracts.
Contracts are executed in the ethereum virtual machine and validated by the miners who include the contract-deploying transactions. The gas spent to deploy the contract and the gas costs of interacting with contracts are converted to fees and paid to the miners. Just like the transaction fees in Bitcoin are rewarded to the miners.
The fees calculate from the gas price * gas amount. Current gas price is around 50,000,000,000 wei, and the minimum gas amount to for a transaction is 21,000 gas, resulting in a minimum fee of around 1,050,000,000,000,000 wei (0.00105 ETH).