You don't need to keep the entire blockchain if storage cost is your concern. It'd be much better for you if you did, because re-indexing requires to re-download the blocks, and you might need to re-index at least once after you're fully synced. Also, it exceeded 500 GB this month.
Of course, I know that Bitcoin Core provides high levels of security, privacy, and stability. But at the same time it consumes a lot of space and memory.Therefore, I have a question: Will the performance of the computer be affected after downloading the entire program with data and consuming the equivalent of about 500 GB, and also consuming part of the RAM?
Not really; new blocks are only mined (and need to be verified by your node) once every 10 minutes, so for the majority of the time, the node doesn't use a lot of power. Do consider that you can also fully shut down Bitcoin Core and let it sync to the top whenever you need to use it.Also, since the size of the data is constantly increasing, will the computer be able to continue running the program after its space exceeds 600 GB, for example? Will the program continue to run, or will we need to replace the hard drive with a larger one?
No, you would need a hard drive replacement (or enable pruning). You could of course also get an extra SATA or even external drive, transfer the blockchain files (after shutting down Bitcoin Core gracefully) and point datadir= to the new location, before starting Core up again. 
