If your config is Keyboard -> Logic -> Origin, there's no way Orign can "do weird stuff in Logic" or "screw up the config of projects", because Logic is not receiving any data from Origin.
If you're talking about the MIDI Thru connector on your keyboard, it does not generate any MIDI data from the keyboard (MIDI Thru is only passsing through the data received on the MIDI IN).
It's not clear what kind of MIDI interface you are using with Logic, but you could indeed connect directly the USB port of Origin to a free USB port of your Mac, as the Origin supports MIDI via USB.
It is not "more stable", it is just a simpler way to go without adding a USB-MIDI interface in between.
Regarding Sync'ing the Origin to MIDI Clock, you have to enable it in the HOME / SETTINGS / MIDI menu: select Global Synchro as "MClock" instead of "Intern".
Then, enable Sync ON for each synchronizable feature (Arpeggiator, Sequencer, Delay, LFO, ...) you want to slave to the MIDI Clock.
(of course, don't forget to enable MIDI Clock Out in Logic for the port where Origin is connected)