In the EU and the UK, yes. Mustard is one of the fourteen allergens that food businesses must declare, which is why it is highlighted in the ingredient list of European packaging. In the United States mustard is not among the major allergens covered by FALCPA labelling, so it can sit unnamed inside a generic spice or flavouring declaration. Reactions to mustard seed protein are real and can be serious, so that labelling gap is the practical thing to know when you are buying imported food.

It grades moderate rather than high, which puts it in the dose dependent band. A pinch in a large batch of something is unlikely to register; a heaped teaspoon in a dressing you eat regularly is worth logging. Because mustard powder is an ingredient inside other ingredients, the realistic risk is accumulation across several prepared foods in a day rather than any single use.

Pure ground mustard seed grades clean on gluten. The catch is the product rather than the spice: English style mustard powders are classically blended with wheat flour, and some prepared mustards use wheat as a thickener. Read the tin, and if it lists only mustard seed you are fine.

Yes. Dry mustard grades clean across the board on FODMAPs, fructans, GOS, excess fructose and polyols, so it is a useful way to add sharpness during an elimination phase. Prepared mustards are a different question, since many add garlic, onion or honey, all of which bring their own FODMAP load.