First, love the game, I actually have a complete set of the 1995 CCG, loved it then too.

1-Demolition run-Accessing a card doesn't apply to ice, right? I.e. can trash anything that isn't ice in the server, right?

2-Cortez-What happens if the corp announces he's rezzing an ice, you trash chip, and he can't afford the 2 extra credits? I assume it stays unrezzed and he keeps the money, right?

Installed ice is never accessed. With Demolition Run, you can trash any card you access, including agendas.

Once the corp says they rez a card, you don't have the opportunity to use Cortez Chip's ability. You have to anticipate.

More elaboration on 2) - Unless a card in Android: Netrunner specifically says it responds to an effect (for example, Decoy's ability to trash itself to prevent a tag), activated abilities can only be used in very specific windows, and not at "instant speed," to borrow a Magic term. I'm going to refer you to the latest FAQ (and updated timing structures) here .

At step 2.3 of the timing structure of the run, approached ice can be rezzed and paid abilities can be triggered. When two players want to do something at the same point in the timing structure, the player whose turn it is goes first, playing all of his desired abilities. So you have to choose to use Cortez at that point. If you don't, then the Corp gets to do all of his things, including rezzing the piece of ice for whatever its current cost is. Thus there's no way to make the Corp spend all of his credits thinking he can rez the piece of ice and then say "Nope, now you can't. It costs two more."