For example, if I set the price as 100,000 token X = 1 Ethereum, and I want to sell 1,000,000 of X, do I have to provide 10 Ethereum as liquidity along with that amount of token X?
Yes because you need to provide equal liquidity for both tokens to pair it. You seem like doesn’t have any idea how DEX and staking on liquidity pool works. You should watch tutorials about this on youtube to make everything clear because there’s a lot of guide video on youtube.
Then, will other people be able to buy 10 Ethereum worth of X tokens?
Yes, that’s your max volume so all the tokens will convert to Ethereum if traders already consume your liquidity but this will not happened since the price impact will be huge before someone can deplete the pool liquidity.
Then, will the Ethereum that other people bought come back to me?
You are confusing, you are the owner of the token which means before other people have your tokens they pay it first to you through buying on your pair except if you do airdrop. So they can sell their tokens to get your ETH stake on the pool.
What happens to the 10 Ethereum that I provided in the first place?
Are they out of my hands forever?
Your ETH will be converted with X tokens if user trade their X to ETH. Again people needs to purchased first your X token before they can trade it back to ETH which means your both X and ETH tokens will be the same at the end and just earn trading fee.