Regarding this, is there trailer parks in Europe?
No, you won't find trailer parks in Europe like you see in the US. Indeed, in many places (like the Scandinavian countries) it would be an outright illegal living situation. In many European countries the government will provide an apartment for you if you can't afford a decent and safe place to live.
Secondly, should I live in a trailer park? Like any other neighborhood, trailer parks can be perfect for you and wonderful places to live, or not for you. Trailer parks are managed communities, and as such, a lot comes down to the management. If the management is great and really cares about making it a wonderful place to live, then it can be.
Accordingly, why are there no mobile homes in Europe?
Mobile homes are pretty rare in Europe. There are slums that carry a similar stigma like this. Many poor in urban areas live in large tenement apartments. In Britain and probably also on the continent there's Gypsies and other groups who live in caravans and travel from place to place.
Why do they call it a trailer park?
So, as a result, you had these folks driving across America now, not only with their automobile, but also with their trailer. And, they're very sumptuous and these people had a lot of disposable income. Cities started building free places to park these trailers and therefore, the name trailer park.