A hash is a short fingerprint of some data: the same input always produces the same string, and changing a single byte changes it completely. That makes it the standard way to check that a download arrived intact, that two files are genuinely identical, or that a file has not been altered since someone published its checksum. This tool computes SHA-1, SHA-256, SHA-384 and SHA-512 for text you type or a file you pick, and can compare the result against a checksum you paste in — useful when the number is 64 characters long and reading it by eye is how mistakes happen. The hashing is done by your browser's built-in cryptography, so even a large file never leaves your device.
No. The file is read on your device and hashed by the browser's built-in WebCrypto implementation. Nothing is sent over the network, and large files are handled at native speed.
SHA-256 unless you were told otherwise — it is the default for software checksums, signatures and most protocols. SHA-512 is a fine alternative and can be faster on 64-bit machines. Use SHA-1 only to check against an old published value, never for anything security-related.
Browsers do not implement it, because it has been broken for years: two different files can be made to share an MD5 hash. Anything relying on MD5 for integrity or security should move to SHA-256.
No. Hashing only goes one way, and the output is a fixed length no matter how large the input. Short, common inputs can still be guessed by trying candidates, which is why passwords need a salted, deliberately slow hash rather than a plain SHA-256.
Download the file again — an interrupted or corrupted transfer is the usual cause. If a fresh copy still fails to match, do not open it: either the published checksum is for a different version, or the file is not the one that was published.