What is the ruling on food products to which a very small percentage of alcohol is added, and what is the ruling on creams, perfumes, and cosmetic products in general?

Alcohol is an intoxicant, and every intoxicant is khamr (wine/alcohol) and forbidden (haram).

Ruling on Alcohol: 1. Impurity (Najāsa): Alcohol is not physically impure (najāsa ḥissiyya); rather, its impurity is abstract (maʿnawiyya). This is the preponderant view. 2. Mixing with other substances: If the effect of alcohol is apparent in the mixture (foods or medicines), its use is forbidden. If its effect is not apparent, its use is permissible. Consuming alcohol alone is forbidden, no matter how small the quantity.

Fatwa of Sheikh Al-Uthaymeen: Alcohol is khamr because of the Prophet's (peace be upon him) saying: "Every intoxicant is khamr." If alcohol mixes with something and does not become absorbed within it, that substance becomes forbidden. If the alcohol becomes completely absorbed and no trace of it remains, it does not become forbidden. The ruling hinges on the effect.

Issue of the Physical Impurity of Khamr: Majority of Scholars: Khamr is physically impure (najāsa ḥissiyya). They based their argument on the verse: "Indeed, intoxicants, gambling, stone altars [for sacrifices], and divining arrows are but defilement from the work of Satan." (Quran 5:90) The Preponderant View: Khamr is not physically impure (najāsa ḥissiyya). The basic principle is that things are pure, and not every forbidden thing is impure (like poison). When khamr was forbidden, Muslims poured it out in the marketplaces and did not wash the vessels. If it were impure, the Prophet would have ordered them to wash them. The "defilement" (rijs) mentioned in the verse refers to an impurity of action (rijs ʿamalī), not a physical impurity (rijs ʿaynī).

Ruling on the Use of Alcohol for Purposes Other Than Drinking (e.g., perfume): It is more cautious to avoid its use in everything (eating, drinking, and anointing), but its prohibition for non-drinking purposes is not definitively established. The reason for prohibition in the Quran (causing enmity and hatred and averting from the remembrance of Allah and prayer) is not realized in non-drinking uses. Piety dictates avoiding perfuming oneself with such perfumes, but a definitive ruling of prohibition cannot be made.