I'm having trouble getting Firefox to send an encrypted message using a certificate, and I've found that the only difference between this one and others that work fine are that this one has a DSA public key while the others have an RSA key. The signature algorithm still says "sha512WithRSAEncryption". I'm wondering if that is causing a problem since the public key algorithm is not RSA.
The signature in the certificate is computed by the CA, and must match the public key of the CA. There is no problem with having a certificate which contains a DSA key while being signed by a CA which uses a RSA key.
There is a big problem, though, with trying to encrypt some data with a DSA key. DSA is only for digital signatures.