Looking at the top 2 pics, I have to say that this box is feeding a 120 volt 20 amp circuit somewhere. Notice only one black wire off the bottom right hand side of the breaker.
Yes. Someone didn't need 220 and just used one breaker to feed 120 to something else (probably an outlet). My first suggestion would be to scrub off all the Sharpie(tm) writing as it is misleading.
That is a 220 2 phase breaker not a good idea!
No, it's 2 single phase breakers clipped at the handles. The 30 amp breaker in the other pictures is a single unit 2 phase breaker. If you pop the clip off of the 20 amp breaker handles you now have two separate 20 amp single phase breakers. BUT... (see below).
If it it's an unused circuit you could put a box next to the panel and install a range receptacle to plug the coupler into.
This box is actually the ideal place to install your phase coupler if that single 120V circuit is not being used.
Leave the two breakers clipped together.
Buy a hardwired phase coupler.
Disconnect the wiring for that 120V circuit and PULL IT OUT OF THE BOX (label it if you can figure out where it goes and can't pull it all the way back to the other end).
Use one of the holes left on top of the circuit panel to install a box large enough to hold the phase coupler you buy (usually a single switch box is big enough). Plug the other hole with an approved snap-in plug.
Wire the phase coupler as instructed to the two breakers.
Re-label the panel "X-10 phase coupler breaker"
Now, if you can manage to go around and label EVERY electrical outlet/hardwired item as to which phase it's on you have a handy-dandy way to easily separate the phases if you need to test for noise generators and such. Just go flip those breakers off and noise should no longer couple across phases (unless you have a non-motor driven 220 device attached to 220 somewhere coupling them and running during testing. Motor driven devices couple somewhat but the rotating magnetic field makes it spotty.).
No need to install a 220 plug (and make sure you have the right one).
Gerald