A miner gets a 'reward' after confirming a block and adding it to the chain, then after 101 confirmations he may use those rewards.
Until then, he is unable to spend the reward.
The 51% is regarding forks mostly, which directly influences who gets the reward for a certain block.
I'm still trying to figure that if it is possible that miners to win rewards purely base on randomness- like a lottery, rather than base on how expensive, and high power equipment...essentially leveling the playing field.
Of course you can. Mining is basically a lottery anyway, better equipment just lets you buy more tickets.