I'm no expert on the subject, but I imagine the timeout exists because users habitually rest their cursors somewhere and since a lot of places have tooltips you wouldn't want it on-screen all the time.
In the past tooltips were no more than a few words, for helpful descriptions you used help popup windows (aka the "What's this" button) which had no timeout but seem to have been phased out in the new Vista HIG documents.
As for #2: It depends on what API you're using to display tooltips (I assume you're a developer?) As for Firefox, besides that "No Tooltip Timeout" extension I can't see anything in about:config, so I guess that's the only way.