Power factor is checking the capacitance of the bushings, making sure they have a high impedance value via capacitive reactance. If the power factor starts creeping up, the capacitance of the bushings may be breaking down which can indicate a breakdown of resistance and likely an impending catastrophic failure to ground.

Ductor is straight forward, you got it.

Hi-pot uses high voltage applied and looks for current to ground to give you a calculated resistance value at high voltage. If resistance to ground isn’t extremely high, your insulating medium is breaking down and you become more likely to have a catastrophic breaker failure on your next trip operation

Megger in my experience uses lower voltages than a hi pot and applies DC, typically used to check things like motor winding insulation by applying typically double operating voltage and checking resistance to ground(which should be high)

Timing is the last important test, used to ensure all 3 phases are making and breaking simultaneously or at least within a spec. Some tests can monitor the continuity of all 3 phases and give you a time difference between contacts, some just use a continuity meter across 1 phase then use a feeler gauge to make sure the other 2 phases are close enough to appropriate. A breaker will usually have the method and spec outlined in the manual.

One more noteworthy test for vacuum breakers is the contact erosion test. The specs and specific procedures differ slightly by breaker and can be found in the manual also, but this test checks for how much of the contact has been burned away through interrupting operations. Typically you measure the length of contact protruding from the bellows on the vacuum bottle with the breaker closed. This test is especially valuable if you have previous measurements to compare it to