You can bind the identity certificate to multiple interfaces. Whether it is self-signed or from a third party trusted root CA it will work either way.
You may get some warnings from ASA if the FQDN or IP address you are connecting to does not match the certificate but clicking through that will allow you to manage the appliance.
Client certificates are a totally separate issue. That's typically only used when you have a PKI and are using the certificates issued to a client as a form of authentication and/or authorization.