Does Eskimo really mean eaters of raw meat ? And even though we fought wars against tribes, in what bad way has the word "Eskimo" been used?

No. Eskimo comes from the Innu-aimun (Montagnais) word ayas̆kimew. It means "a person who laces a snowshow". It is still in use in Alaska as a word to describe all Alaskan Native peoples (Inuit, Yupik, Aleut, Athabascan etc) but in Canada and Greenland Inuit has been used since 1977. It was not offensive in origin, or by meaning, it just isn't the name most of the circumpolar peoples use for themselves.

There is no such thing as "westernized languages". There are Indo-European (formerly called Aryan) languages, and most European languages today are in the Indo-European group, but so are Persian/Iranian and most of the languages of India. 

There are also Uralic languages like Estonian, Hungarian, Finnish and Sami, but other Uralic speakers are in Northern Asia. 

The language of the Basque people, Euskara, is an outlier, the last surviving language from a family that otherwise went extinct but was probably found in a much larger area of Europe thousands of years ago.

European languages is a geographical term meaning "all the languages currently spoken in Europe", while Indo-European and Uralic are actual linguistic terms for clusters of recognizably related languages, regardless of where the speakers live.

Barbarian means someone who eats raw meat and drink blood. 

The term Eskimo was once common, but is now sometimes perceived as derogatory, especially in Canada. In Alaska, however, the term Eskimo is commonly used, because it includes both Yupik and Inupiat, while Inuit is not accepted as a collective term or even specifically used for Inupiat (who technically are Inuit). No universal term other than Eskimo, inclusive of all Inuit and Yupik people, exists for the Inuit and Yupik peoples.

The primary reason that Eskimo is considered derogatory is the questionable but widespread perception that in Algonkian languages it means "eaters of raw meat". One Cree speaker suggested the original word that became corrupted to Eskimo might indeed have been askamiciw (which means "he eats it raw"), and the Inuit are referred to in some Cree texts as askipiw (which means "eats something raw").

"Europeans speak westernized languages"

I'm not sure what you are trying to say here..

> What do they expect to be known as, by westerners ?

They prefer to be known by the names they use themselves for their ethnicities: Inuit, Yupik...

Yes.  However, that term was coined by outsiders, and is now considered offensive.