Is it safe to paste a token here?
The token is decoded and checked in your browser; nothing is sent anywhere or kept after you close the window. Even so, a live token is a password for as long as it lasts: prefer an expired one, or one from a test system.
Why does my signature not verify?
The tool names which of the usual causes it is: a public key where a secret is needed or the reverse, the wrong curve, a secret that was meant as Base64, an ECDSA signature in DER instead of r and s, or a token changed after signing.
What is the algorithm confusion attack?
A server that lets the token choose the algorithm can be sent an HS256 token signed with its own public key as the secret. The tool tries exactly that when you give it a public key, and names it when it verifies.
Is a JWT encrypted?
A signed JWT is not: anyone who holds it can read every claim, which is all this tool does before you give it a key. Only the signature needs the key, and only an encrypted token (JWE) hides its claims.