It can remove printing, copying and editing limits from a PDF that opens without a password. It can't open a PDF whose password you don't know. Unlock only PDFs you have the right to unlock.

No. The password stays in this browser tab. It goes to the unlocking engine on this page and nowhere else. The page's security policy blocks it from sending data anywhere, and the page never saves or logs the password. The field is cleared as soon as you use it.

No. Only the lock is removed. The pages, text, images, forms and bookmarks come out the same, and your original file is not touched.

Some PDFs only look protected. If this page says there is no lock, the file has no password and no limits, so you can use it as it is.

Both kinds: the password that opens a PDF, and the owner limits on printing, copying and editing. It works with the encryption in common PDF files, from old 40-bit files to 256-bit AES.