A smurf? The Blue Man Group? Dr. Manhattan?

Dr. Tobias Funke.

Ich bin blau, da ba dee da ba die, da ba dee, daba die

An avatar!

A sad man? With blue as in "blues"?

I'm thinking the movie "Avatar"

no, that's not possible here. As you say the frase is: Ich bin blau. Du bist blau. blau sein.

• Ein blauer Mann, reminds more of ein Blaumann than of being drunken, that's a blue working suit for non businessmen.

• There are also other frases with 'blau' like 'blau machen' ~ having a break.

Because 'ihr' is plural 'you' when used as the subject. It's 'her' when used as the the direct object (Der Mann mögt ihr)

It would be then: "Sie mag den blauen Mann"

When adjectives are on the other side of a linking verb, they don't change ("Der Mann ist blau"); that's called a "predicate" adjective. But when they are right next to the noun they're modifying (called "attributive"), they change form to match the gender, number, and case of the noun. So "blau" becomes "blauen" for the same reason that "der" becomes "den": it's the masculine accusative form.

Note that adjectives have multiple declension patterns, depending on definiteness - if you have a definite article, like "den" in this case, you use the "weak" pattern, in which the only two endings are -e and -en: -e for masc/fem/neut nominative and fem/neut accusative, -en for everything else. See http://en.wikipedia.org/wiki/German_declension#Attributive_adjectives

Same basic meaning, different emphasis. Similar to the effect of the English "It's the blue man you like."