1. Can snare be advanced, or does a trap have to specifically say this card may be advanced, before it can be advanced?

It depends on how the advancement counters are being placed. The Advancement action requires a card that may be advanced such as an Agenda. On the other hand, a card like Mushin No Shin PLACES advancement counters and as such does not require the card be advanceable (like an Agenda or a card that says it can be advanced such as Weyland advanceable ice).

“Can be advanced” is the act of spending a click and a credit to place an advancement token. Unless otherwise specified, ONLY agendas can be advanced. If a piece of ice, asset, or upgrade can be advanced, it will say so. Snare does not, so you can’t normally advance it.

There are certain card effects which move or place agenda counters, but they are distinct from corps’ native ability to advance cards.