Can it remove a password I don't know?
No. If the PDF needs a password to open, you must supply it. Restriction-only PDFs (which open fine but block printing or copying) usually unlock without any password.
Why is entering my password here safe?
Because it never leaves your device: decryption runs in your browser through the qpdf WebAssembly engine, with no server involved. You can verify in your browser's network tab that nothing is transmitted.
Does unlocking change the document's content?
No. Pages, text, and images are untouched. Only the encryption layer and usage restrictions are removed.