CSR generator — certificate signing request and private key

Because browsers have not read the Common Name since 2017. Chrome dropped the fallback in version 58 and the others followed, so a certificate whose domain appears only in the CN matches no hostname at all. Some CAs quietly copy the CN into the SAN when they issue; many just reject the request. Putting it in both places removes the question.

Only for organisation-validated (OV) and extended-validation (EV) certificates, where the CA checks them against your legal registration and will reject a mismatch. For an ordinary domain-validated certificate — which includes everything from Let's Encrypt — they are ignored, and leaving them empty is fine.

Usually not for a web server. An encrypted key must be unlocked at every start, so the server cannot come back up unattended after a reboot — which is why nginx and Apache are almost always configured with an unencrypted key protected by file permissions instead. Encrypt it if you are going to move it between machines or store it somewhere shared.

Yes — write *.example.com. Note that a wildcard covers exactly one label, so *.example.com matches www.example.com but neither example.com itself nor a.b.example.com. If you need the bare domain too, list it separately. Public CAs also validate wildcards through DNS rather than HTTP, so issuance needs access to your DNS records.

ECDSA P-256 gives roughly the security of RSA 3072 with a much smaller key, which means faster handshakes and less CPU per connection. RSA 2048 is supported by absolutely everything, including old appliances and some payment terminals. If you control the clients, ECDSA; if you cannot be sure what connects, RSA.