1. From OEM it appears our 11gR2 database is not running automatic "optimizer stats gathering"
2. Also from dba_feature_usage_statistics.CURRENTLY_USED is FALSE
question: how do we turn on features, that are not running, such as "optimizer stats gathering"
The question has not much to do with EM but is database related.
For the answer see http://docs.oracle.com/cd/E11882_01/server.112/e16638/stats.htm 13.2.1 Enabling and Disabling Automatic Optimizer Statistics Collection
That's not entirely correct. Auto stats collection is part of the auto-task framework job that can be enabled via EM. If you tell me which versuion of EM, I can tell you how to enable it via EM.
As mentioned before you can find your answer in the link.
In the concerned database you can enable the automatic optimizer statistics collection by (as user sys):
client_name => 'auto optimizer stats collection',
operation => NULL,
window_name => NULL);
You can querie DBA_AUTOTASK_CLIENT to see if the task is now enabled.