If I add cooked grape juice to vinegar, does the juice undergo fermentation and also change to vinegar? Are there other conditions like exposure to air? How long would such a process roughly take?
The process that transforms sugars (e.g. the ones in grape juice) into ethyl alcohol and then this latter into acetic acid is a biological one, that is, performed by micro-organisms. The first step is usually performed by yeasts such as Saccharomyces Cerevisiae, whereas the second step is performed by bacteria of the Acetobacter genus. Thus, your grape juice won't change to vinegar if you mix both liquids. All you will get is a sweeter vinegar, or a sour grape juice.