I have doubts about master nodes and miners in Ethereum.
1- Do all the miners have to be full nodes as well?
2- Do all the full nodes have to be miners as well?
There are no master nodes in Ethereum, there are just nodes. All a miner does is hash block headers with different nonces, trying to generate a low enough hash. All a full node does is download new blocks and
Miners do need access to a node in order to generate the blocks/block headers that they hash, but they don't need to be nodes themselves. Nodes are not miners, but they do need miners in order to get new blocks.