Heat oil in large nonstickskillet over medium heat.
Add onion andstir 1 minute to coat with oil.
Add vinegarand sugar and stir until onion begins tosoften slightly, about 3 minutes.
Transferonion to baking sheet or platter; spread insingle layer.
Sprinkle with salt. Cover andchill at least 8 hours or overnight (onion willturn pink). DO AHEAD: Can be made 2 daysahead. Keep chilled.
Whisk red winevinegar, 1/4 teaspoon salt, 1/8 teaspoonfreshly ground black pepper, and sugar insmall bowl. Gradually whisk in both oils.DO AHEAD: Vinaigrette can be made 1 dayahead. Cover and refrigerate. Bring to roomtemperature and rewhisk before using.
Combine Portand figs in large saucepan. Bring to boil.Reduce heat to medium-low and simmeruntil figs are plump and tender, about30 minutes. Using slotted spoon, transferfigs to small bowl. Increase heat tomedium-high and boil Port syrup untilthickened and reduced to 6 tablespoons,about 8 minutes.
Transfer syrup toanother small bowl. DO AHEAD: Can bemade 2 days ahead. Cover figs and Portsyrup separately and chill.