ERROR: Kerberos authentication via krb5.keytab against local SMBD doesn't work
kinit: krb5_init_creds_set_keytab: Failed to find dns-xs1-ucsdc@T4DLAB.HOME in keytab FILE:/var/lib/samba/private/dns.keytab (unknown enctype)
ERROR: DNS update via Kerberos doesn't work on this server
That first message is very bad indeed, and the third one is most likely a direct result. It also matches what you've described in your posts so far.
I don't have a good suggestion for how to fix this. However, there is the possibility to re-provision Samba 4 from the data in the master's LDAP directory. As this re-builds the whole Samba 4 data the Kerberos thing might get fixed, too. However, I don't know what kind of an effect this will have on existing Windows clients. But it most likely won't get worse than it already is; Kerberos is a central component of any Active Directory domain and it not working is basically the sky falling down.
A safer but or course more expensive option is to contact Univention's Professional Services (their support) and letting them fix this.
That's normal. The default/first site in any Active Directory domain is always called "Default-First-Site-Name".