Is it safe to paste a CSR into a website?
A CSR holds only public information: the names, the public key and a signature. On this page it is not sent anywhere either, because the decoding and the signature check run in your browser. Never paste a private key, here or anywhere else; the decoder refuses to read one.
What does “signature verified” mean?
The CSR was signed with the private key that matches the public key inside it. The decoder checks this with your browser's Web Crypto API. A mismatch means the request was changed after it was signed, and a certificate authority will reject it. A few algorithms, such as DSA or SHA-224, cannot be checked in a browser, and the decoder says so instead of guessing.
Does a CSR contain my private key?
No. It carries only the public half. If the text you have includes a line such as BEGIN PRIVATE KEY, that part is your private key and should stay on the server.
Why does my CSR have no subject alternative names?
OpenSSL only adds them when asked, with -addext "subjectAltName=DNS:example.com,DNS:www.example.com" on OpenSSL 1.1.1 or later, or a subjectAltName line in the request config. Most certificate authorities copy the common name in for you, but listing every hostname yourself avoids a certificate that misses one.
Can it decode a certificate as well?
Yes, a certificate pasted here is decoded too. The certificate decoder is built for them, though: it reads whole chains, checks each signature against its issuer, and counts the days left.