TLS_DH_RSA_* cipher, how can static DH use an RSA certificate?
Look at TLS 1.0 Section 7.4.2, DH_RSA means a DH certificate which itself is signed using RSA by a CA.

The server has a static (long term) DH keypair. The public is included in a certificate and signed by a CA using RSA.

In the handshake, the server sends the certificate which includes the server's static DH public, signed by CA using RSA.

The client verifies the cert chain using RSA like normal, generates an ephemeral DH keypair, performs DH computation against the server's static DH public, computes shared premaster secret. The client sends the client's ephemeral DH public in the ClientKeyExchange.

The server receives the ClientKeyExchange, performs a single DH computation, and computes the same shared premaster secret.

There is no asymmetric encryption or online asymmetric digital signature operation in the handshake - only the DH operation.

This is historic, right? You're not going to use it, right?