No, there are simply too many. Even gold has an E number (175).
People with allergies do remember the specific E numbers they have to watch out for.
The packaging often states what the E numbers are, either specifically or the general category (stabilizer, emulsifier, preservative, colouring, taste additive, ...).
Nope, but E150 is pretty well known because it is ... everywhere. But we do know that if whatever you buy has to many E numbers on its label its probably something you do not want to eat (That's a rule of thumb: Everything, even water, has a E number, but companies usually only put them on the labels for the not-so-nice stuff)
As a side note, do Europeans memorize what each E number is?