Which E-numbers are halal and haram ? Which E-numbers are allowed by Islam ? Which products contain ethanol and are haram ?

Good questions between science and faith (Islam teachings) 

I assume when you talk about "halal" and "haram" that you are about consuming (eating/drinking) food and drinks that include these things. 

Let me share with you my approach to this .... 

Whatever is haram is very well-defined in Islam and it is based on the effect/impact it leaves on "mental awareness" that is necessary to differentiate between good and evil.  Then, whatever is proven to be Haram in this sense, would not be allowed, even in small quantities/concentrations that may not cause this effect to happen ! However, if such materials (ingredients) enter into a chemical reaction (in the final product) that changes their "haram" characteristic ... then  it is NOT haram anymore Good example of that is (1) grape juice (halal) ... turning into (2) wine (haram)  .. turning into (3) vinegar (halal once again)