For example:
VIKTOR 2.0:
Hosted Power Counter: Do 1 brain damage
Aggressive Secretary:
trash 1 program for each advancement token
Can I advance a card that makes use of Hosted Power Counters in the same way that I can advance an agenda or a card like Aggressive Secretary?
Power counters don't (currently) interact with anything other than the card that placed them. A card will define when to place a power counter, and the effects of having them on itself. EG Draco lets you pay to place power counters when it's rezzed, and they boost the strength. The most complicated one currently is Personal Workshop which places power counters on hosted cards, but these cards are inactive while on the workshop, and so the power counters are only referenced by the personal workshop which placed them.
So no, you cannot interchange advancement and power counters.
Advancement and Virus counters are two specific types of counters which a range of cards let you place/remove/move. You can use Trick of Light or Shipment from SanSan to place or move advancement counters. The corp can clear all the virus counters, the runner can play Surge! to place extra virus counters.
No. An advancement counter is completely different then a power token or a virus token. This is why cards specifically list power or advancement counters when they talk about something.
As a rule of thumb, advancement counters are movable, but power counters and virus counters are usually used more as placeholder counters rather then a tangible thing in the game.
