In EOS, will the voter get money if its voted node becomes the proposer?
Also, how is the proposer itself rewarded?
I'm assuming by node you mean block producer. If the block producer agrees to pay the voters a share of the block rewards, then yes, a voter will get money. However, it's been my experience in the EOS community that this is frowned upon, as most community members suggest the block producers with the best tech to support the block chain should be voted in, not those incentivizing via a share of the rewards.
A block producer is reward via block rewards, similar to Ethereum and Bitcoin.