Is the file really encrypted, or just marked read-only?
Really encrypted. The page content, the strings and the metadata are all encrypted with AES-128 under the standard security handler at revision 4, and the file cannot be opened without the password by any reader. You can watch the tool prove it: it re-opens the finished bytes with no password, which must fail, and then with your password, which must succeed.
Is this AES-256?
No, and we will not imply otherwise. It is AES-128 at revision 4. The library used here can also write revision 5, but revision 5 is Adobe's withdrawn Extension Level 3 whose password check is a single SHA-256 — weaker in practice than what ships here. The AES-256 that PDF 2.0 actually standardised, revision 6, is not implemented by it. If AES-256 is your requirement, this tool is not the right one.
Why does it refuse my password?
Because the encryption is only as strong as the password. Revision 4's key derivation is 50 rounds of MD5, which is cheap to run over a guess list, so a short password is the whole attack. Empty passwords, anything under six characters and short runs of digits are refused; a passphrase of several words is far stronger than a clever short one.
What happens if I forget the password?
The file is gone. There is no recovery, no back door and no copy of the password anywhere — it exists only in this tab while you type it. That is what makes the protection real, and it is also why you should write the password down before you close the page.
What do the permission settings do?
They record what a reader is allowed to do once the file is open: copying text, printing, changing it. They are enforced by the reader rather than by mathematics, so treat them as an instruction to well-behaved software, not as a guarantee. The password is the part that cannot be argued with.
Can I protect a file that already has a password?
No. An encrypted PDF cannot be read without its password, so there is nothing here to re-encrypt. Open it in a reader, save an unlocked copy, and protect that.