If I delete old game saves on the 360 will my achievements and gamer score go away? dumb question?

No.

Achievements and gamer score are in the cloud, they ain't never going away!

Quasi-related question: isn't there supposed to be a way to delete zero-gamer score games (or maybe it's just Arcade demos) from your list of games played? How do you do that?

"First, press the Xbox 360 Guide button (the big glowing button in the middle of your controller). This will bring up the new guide. Scroll left to the Games blade and select Achievements. Press the "X" button to delete any game from the list with a Gamerscore of zero. You will be asked to confirm the action, and then you are done. Thankfully, this can only be done on games with a score of zero; otherwise, you could remove your ever-so-important achievement points."

Source: http://www.associatedcontent.com/art...ore_games.html