Systemd Core Dumps – How Can a Non-Root User Retrieve Core Dumps?

From the docs on coredump.conf,

To disable a configuration file supplied by the vendor, the recommended way is to place a symlink to /dev/null in the configuration directory in /etc/, with the same filename as the vendor configuration file.

sudo ln -s /dev/null /etc/sysctl.d/coredump.conf
sudo systemd-sysctl 

Since systemd, things are managed differently.

The systemd-journald man page explains how journal access control is done:

Journal files are, by default, owned and readable by the "systemd-journal"
system group but are not writable. Adding a user to this group thus enables
her/him to read the journal files.

By default, each logged in user will get her/his own set of journal files in
/var/log/journal/. These files will not be owned by the user, however, in order
to avoid that the user can write to them directly. Instead, file system ACLs
are used to ensure the user gets read access only.

Additional users and groups may be granted access to journal files via file
system access control lists (ACL).

Fedora 20 uses ACLs to give users in the adm and wheel groups read access to all the journals.

how to give a normal user also access to the root journal?

Run setfacl -n -m u:username:r /var/log/journal/*/system.journal .

how to get list which journals are available for a given user?

You can su to the user and run journalctl --header|grep '^File Path' to see the names of the journals he or she has access to.

getfacl can be used to see which groups and users have access to journal files. I don't know of a simple way to list the files that are readable by a specific user.