[Ethereum] how to deal with race condition and execution times of a contract

Yes. Think of contracts like objects in an Object Oriented language. From a single contract you can create multiple instances if you like. When you deploy a contract it returns a unique address you can use to talk to it through the web3 API.

Looks like a horrible example.

To begin with, there is zero talk about how much Ethers the users are sending with their transactions. That's what matters, because the code makes checks against msg.value. It simply looks like the writer has mixed up msg.value with the price (or new_price) parameter.

I'm not sure if you can call anything in the blockchain a race condition. I guess, maybe, you can, if two transactions try to do the same thing which only one can do. But the term "race conditions" is usually used when there is some degree of parallelism, and the blockchain has zero parallelism when executing transactions.

Anyway, if in the example there was a function which buys as many tokens as the caller can get with X Ethers, it would be a different story. Then an attacker (owner) could enter a transaction which makes the token price higher, and this transaction gets mined before the buyer's. This basically happens in decentralized exchanges all the time, in a bit more complicated manner.

Furthemore, transaction are not "sent to a block". They are sent to a pool of transactions, and the miners decide in which block to include which transaction.