Yes. Sake is brewed from rice, water, koji and yeast, with no barley, wheat or rye anywhere in the process, and it is graded gluten free here. The koji mould itself is cultivated on steamed rice. The caveats are the usual ones for any prepared drink: flavoured or fruit sakes, sake-based cocktails and cooking sakes with added seasonings can bring in other ingredients, so read those labels.

Far less. Sake grades borderline for sulfites where wine grades high. Winemakers add sulfur dioxide as a preservative and antioxidant, while sake brewers generally rely on pasteurising the sake twice instead, so most bottles carry only the trace sulfite that fermentation itself produces. Note that low is not zero, and a handful of exported sakes do add sulfites and will say so on the label.

It is moderate, not high, and it is graded lower than both red and white wine. Because sake is fermented and never distilled, the amines made during brewing stay in the bottle, so it grades borderline on histamine, on histamine liberation and on tyramine together. If wine is a reliable trigger for you, sake is worth a small controlled test rather than an assumption in either direction, and the pasteurised mainstream styles are a more predictable starting point than unpasteurised namazake or long aged koshu.

Usually not because of sake. Roughly a third of people of East Asian descent carry a variant of the ALDH2 enzyme that slows the breakdown of acetaldehyde, causing facial flushing, a racing heart and a warm prickly feeling with any alcohol at all. That reaction follows the drinker rather than the drink. Sake can add to it, because its borderline histamine and histamine liberation grades contribute their own flushing on top, but the underlying flush is an alcohol response and not a sake specific one.