@#7. Hi Reinhard W.
"Hautausschlag" is as non-specific as "rash" (or "skin rash", if you must). In both languages it applies to skin involvement in infections as well as a whole range of primary and secondary skin diseases.
"Ekzem"/"eczema" may be used generally in both languages as a lay term for inflammatory skin conditions - not infections - but I would reserve it for cases I actually knew to be atopic dermatitis/eczema.
"Dermatitis" is often used synonymously with "eczema" in English but, again, that is a generalisation in lay terms. On the basis of meaning "inflammation of the skin", "dermatitis" could refer to most rashes, but it isn’t used that way – I would keep it for instances such as
types of dermatitis and specific cases such as "contact dermatitis", "seborrhoeic dermatitis" (cradle cap), atopic dermatitis (eczema) etc.
For measles or chicken pox, for example, or Spike's urticaria, you would definitely say a rash and not dermatitis or eczema.