Question on Oracle OEM version and plugin version upgrade
Plugins are deployed on the OMS and the agents as well. First you should upgrade the plugin on the OMS, then on the agents.
You don't need to upgrade between versions sequentially, you can upgrade to the highest available.
Yes, there are. Currently 12.1.0.5 is the latest version, and there are quarterly PSUs as well. Check the below MOS note:


Oracle Recommended Patches (PSU) for Enterprise Manager Base Platform (All Releases) (Doc ID 822485.1)

There is no PSU released for 12.1.0.5 yet.