Yes. Distillation separates the alcohol from the grain and leaves the gluten protein behind, so distilled spirits, including whiskey and vodka made from wheat or barley, are gluten-free and generally safe for celiac and gluten-sensitive drinkers. The exceptions are spirits with flavorings or ingredients added after distilling, so check anything that is not a plain bottle.

Generally yes. Distillation removes most of the histamine and sulfites that fermentation and ageing build up in beer and wine, so a plain spirit carries very little. But alcohol itself slows DAO, the enzyme that breaks histamine down, so spirits can still trigger histamine symptoms, just usually less than a glass of red wine or a beer would.

Clear, unaged, unflavored spirits like vodka and plain gin tend to be the gentlest, because they carry the least histamine, sulfite and congener load. Aged spirits (bourbon, whiskey, brandy) and anything sweet or heavily botanical carry more. Whatever you choose, keep the pour small, since the alcohol itself is the main driver.