These three questions are related and are discussed here combined.
The list of really prohibited E-numbers is very short; E120 and E904 as these are made of or contain insects. E901 is made by insects, like honey, but does not contain insects and thus is generally considered halal.
All other E-numbers are basically permitted and also widely used in Islamic countries. However, this does not mean that all additives are always halal. In many additives fatty acids are used in the production. And it is a matter of concern for many Muslims where these come from. If these are from plant origin, they are halal, if they are from animal origin they may be halal or haram, depending on the animal, see also below. Chemically they are identical, from the chemical composition it can not be determined whether animal or vegetable fat has been used. Only the producer and/or ingredient supplier is able to provide this information.
Another complication is that additives can be listed by their chemical name or by their (E-) number. In the EU the producer has to provide the name or the number or both. Outside the EU many countries use the same numbering system, but generally without the E, and in other countries only the chemical names are used. The list of additives that may be of animal origin, or may contain fatty acids that may have been derived from animal origin, can be found here. In that list also the chemical name is provided.
Fats, whether from plant or animal origin, consist of glycerol and generally 3 fatty acids. Fats can be split in fatty acids and glycerol (the same reaction also takes place in the intestine when fats are digested). The fatty acids can be purified and reconnected to glycerol as mono- di- of triglycerides (glycerol with 1, 2 or 3 fatty acids respectively). Many additives consist of these semi-natural fats, which act as emulsifiers.
These semi-natural fats are degraded and metabolised in the body, just as normal fat.
Chemically the fatty acids from animal or plant origin are identical. Therefore the origin is of no importance for the function in the food. Producers thus normally choose the cheapest oils to make these fats. This is generally some vegetable oil, which makes the additives halal. However, animal fats can not be excluded and thus the same additive may be sometimes haram.
In the Islamic world there are several additional discussions on additives containing fatty acids. Here we will mention the two points of issue, but, unless there is agreement among Islamic scholars, we do not further elaborate on the arguments of all parties concerned.
The first issue is the presence of animal fatty acids. If this fatty acid originates from pork, it is generally considered haram. If it is from other animals, it is generally considered halal. However, there is a discussion whether animal fat from other animals as pigs, is halal when the animal is not slaughtered in the prescribed Islamic way.
The second issue is whether the presence of fatty acids originally derived from pork, makes the additives haram. The final additive, as present in the products, is not present in pork (it is not a natural component) and thus is not by definition haram.
The first issue limits the use of many additives and/or complicates the matter for many Muslims, the second discussion actually makes it easier for many Muslims to choose products.
Alcohol and ethanol
According to Islam the use of alcohol is forbidden, as it may influence the mind of the person and thus his behaviour. Unfortunately when the Quran was written, the word alcohol did mean only ethanol. Nowadays, chemically, alcohol means all chemical components with an -OH (or alcohol) group. Unfortunately in common daily language, alcohol means either ethanol, or any drink with a certain percentage of ethanol. For religious purposes and in daily life ethanol and alcohol thus are identical, but for chemists ethanol is just one of many alcohols.
Ethanol is produced during the fermentation of a product by (mainly) yeasts. In most cases this results in very low percentages, and these are not influencing the brain. In products such as bread, yoghurt, kefir and similar, ethanol is produced during the production. Still, these products are halal, as the percentage of alcohol in the final product is extremely low. It is impossible to get drunk from these products. In those cases where sufficient amounts of alcohol are produced, such as wine, beer and spirits, the percentages are high enough to get drunk, these products thus are haram.
Vinegar is a product which is traditionally prepared from wine or other fermented liquids. During the fermentation, the ethanol is converted by the bacteria into acetic acid. The final vinegar thus contains only traces of ethanol. Again, you can not get drunk from vinegar, and vinegar is considered halal. Modern vinegar can also be made chemically and never contained ethanol. Traditional vinegar thus is often referred to as wine vinegar or similar, which may be confusing. Wine vinegar does not contain wine or ethanol, it simply indicates that is is made of wine and not made chemically.
Sugar alcohols are sweeteners, also known als polyols. This category includes sorbitol, xylitol and a number of other products, all with a name ending on -itol. These products are made of sugars and chemically the aldehyde or ketone group in the sugar is converted into an alcohol group ( =O is converted into -OH). Here alcohol stands for the chemical group and has nothing to do with ethanol, the forbidden form of alcohol. Sugar alcohols thus are halal.