When a value is stored in a session object, how long is the cookie life (ref. Active Server Pages 3.0, chapter 26)?
Will the cookie be deleted once the session times out?
Is the cookie in a file located on the local browser PC's hard drive?

Cookies are usually written onto the client browser, its totally session independent, you can manipulate when you want the cookie to be expired, for example you can do something like this for the cookie not to expire ever!

Response.Cookies("name").Expires = Date + 365

and yes the cookie is located on the local browser pc's hard drive, do this
 goto tools->settings->view files

all the cookies are stored with a prefix of cookie.

Chints.