OK. So when you hit Done before, it was armed. so the keypad should have been in armed state.
Once the keypad and HSM are both disarmed, hit Done in HSM. Then arm from keypad, and see if disarm works from keypad.
To tell HSM state, you either need to open the app, or refresh the Apps page. The Apps page is not dynamic. For that matter neither is the app page. Both need to be refreshed to see the current state of HSM.
Negative. Either will arm the HSM just fine with the other keypad following the HSM state. Neither will disarm so long as a trigger exists for key code entry without adding the HSM disarm action.