Generate a random password of any length from the character sets you choose, or a memorable passphrase of random words. Every password is drawn from your browser's cryptographic random source, is never transmitted or stored, and comes with an entropy figure so you can see how strong it actually is.
At least 16 characters for anything that matters. Length beats complexity: a 20-character password of only lowercase letters has more entropy than a 10-character one using every symbol on the keyboard.
Yes. They are generated in your browser from the Web Crypto API, never sent over the network and never stored. You can disconnect from the internet before generating one if you want to verify that.
They are easier to remember and type at the same strength, which matters for the handful you must memorise. Six random words give about 77 bits of entropy - comparable to a 13-character random password. For everything else, use a password manager and long random strings.