Many recipes call for wine. Has anyone authoritative written about the halachic status of cooking with wine in the nine days? Would it matter if the alcohol were cooked off?
It's appropriate to be careful not to eat food kneaded with wine or grape juice from rosh chodesh [Av] and on.
In a footnote, he indicates that this comes from applying Magen Avraham 551:29 — that food cooked with meat is forbidden by custom — to wine. He then notes that Mishna B'rura :63 allows such meaty food if the meat is less than (or equal to) 1/61 of the whole dish, but demurs at applying that leniency to wine kneaded into dough, since women knead dough. He also cites Or'chos Chayim (in the name of the M'ore Or) as indicating that one should not eat fish cooked in wine.
In answer to your 2nd question, if the wine is "cooked off", I think that the issue in Mishnah Brurah, mentioned above, is if something obtains the taste of wine. MB does address "chometz" or vinegar, stating that it's OK to use wine vinegar, despite the fact that it is made from wine. That's b/c vinegar does not have the taste of wine, and people don't drink vinegar. In short, the prohibition of wine is that it is pleasing.
Thus, even if the alcohol from the wine is "cooked off", the food probably has the taste of the wine. Onion soup, and wine in a fish sauce obtains the taste of the wine. I don't know, though, if there is a certain minimum volume that may apply to this "obtaining wine taste" rule. Perhaps, it depends both on the food and type of wine. (IMO, Manischewitz Malaga should be prohibited even NOT during the 9 days :-)