What is the maximum voltage permitted when MOC3061 is "on"?
When the junction is closed (not current activated), its practically a big resistance in circuit, 


No, we call that an open-circuit. It comes from the days of switch contacts. Switch open = contacts separated = no conduction.







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Figure 1. Open and closed switches.


  ... that supports maximum up to 600 V in this case to not get damaged. 


In the off-state (open-circuit) the device's triac can withstand 600 V.


  But what if the junction is "on" (it's Gate/Base is open) and the same 600 V are applied?


The device you have referenced contains a triac. It doesn't have a base. 







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Figure 2. (a) Incorrect application. (b) Correct application.

You never apply 600 V to a triac (or any other switch) without some form of current limiting. In Figure 1a the fuse would blow when D1 is turned on - if the triac doesn't blow first. In Figure 1b the lamp will limit the current to a safe value and the voltage across TRI1 will fall to about 1 V AC. The high voltage will be dropped across the lamp.







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Figure 2. An equivalent circuit for Figure 2. When the switches are open, as shown, the full voltage appears across the switch. If you close SW2 the voltage across the switch falls to zero. If you close SW1 you may see some voltage across the switch because of the huge current flowing through the contact resistance.


  Is the same thing as when is in "off" mode? It's the resistivity of the metals + some conductivity in play? 


No. Triacs are made of semiconductor material - silicon.


  Then I should ask, what is the maximum voltage permitted when is "on"? Still 600 V maxim (in this case) or greater (because of conductivity)?


As explained, the voltage when on is only about 1 V or so. You will find the value in the datasheet.

You may wish to revisit your previous question. I don't think you understood any of the answers.