The wine stays in the primary until most of the fermentation is done. At about 1.020 SG or so, it goes into a carboy. This is apparently a rule of thumb that my Texas persimmons didn't get the memo on, though, as I racked it and zip, boom, it started right up and fizzed up through the airlock. It's currently in time out in a primary again :-). The moral of the story is that it's a good idea to check on the wine you've racked a few hours after putting it in its closet lest you have a sticky mess all over (no, mine didn't get to that point).
As for extracts....what kind are you thinking of using? Most anything you'd find in an extract can be added to a primary and the wine flavored that way.
Considering: Sparkling raspberry wine, carrot wine
In Primary: Ed's Apfelwein; Raspberry Puree Apple Cider
In Secondary: Pumpkin Pie Mead; Traditional Mead; Dried Elderberry Wine; Blueberry Wine; Texas Persimmon wine; White grape/peach wine; Texas Twang; Hi, Biscus! Metheglyn; A Maize-ing Wine
So far, so good.