How can I know if a food or ingredient contains yeast or yeast-producing ingredient? My condition requires yeast-free foods and ingredients.
There are no "yeast-producing" ingredients - either you have yeast present or not.
Yeasts are fungi that live on many plant-based ingredients. Whether they will multiply depends on the environemental conditions.
Without discussing medical aspects (which are clearly off-topic here), you might expect natural yeasts on the skin of most fruit and grains, they are the reason that these can be fermented1 without adding yeast from another source. Heat kills live yeasts, but the required temperatures are different depending on the strain. Classic baking yeast starts to die at around 50°C for example, boiling your food should eliminate them.
And then theer are the typical foods that have yeast added, which are baked goods and alcoholic beverages. Many of these are heated, thus killing he yeast, but not necessarily so for some beers and some (young) wines may still contain a few live cells. A dietician should be able to answer this in detail.
1 e.g. in the production of alcoholic beverages like wine and beer or for sourdough in baking