In UCS you can add LDAP schemas to the server by using the udm settings/ldapschema module.
However, before you do that I suggest you take a look at Univention's extended attributes. Univention recognizes the need for user-controlled LDAP attributes and provides a set of 20 pre-defined LDAP attributes just for this case. The admin can configure each of those attributes to be accessible in the Univention Management Console (the web interface) and the Univention Directory Manager (the command-line management tool for the domain, udm). You can configure the name it is listed under and various other aspects.
In the LDAP those attributes are named »univentionFreeAttribute1« through »univentionFreeAttribute20«.
The schema for these custom attributes is always active, so you can start using them right away.
On a UCS system there are actually two LDAP servers running: one from the Samba 4 service (that's the Active Directory portion of a UCS) and the OpenLDAP one. The OpenLDAP one listens on the port 7389.
So connecting to that server can be done with the usual commands:
ldapsearch -x -h hostname-of-the-ucs-master -p 7389 -D uid=…,cn=users,dc=… -b ldap-base-dn -W
You can look up your LDAP base DN with the command »ucr get ldap/base«. Note that the OpenLDAP is configured not to allow anonymous binds by default, meaning you have to use a bind DN with -D and provide the appropriate password. Often we create a single user for this purpose, e.g. called »ldapsearch« or something similar.
As far as I've understood their changes to the licensing: yes, you're fine. The core edition is free to use however you want. Take this with a grain of salt, though, as I'm not a Univention employee.