You want to taste your lips again
It means "I want to be in love again".
Quiero verte otra vez
"Te quiero como a ninguna otra."
No quiero volver a verte otra vez
¿Quieres otro más?
"Otra chica" means another girl.
otra means "other" but the other word is not Spanish.
another beer
That means "another one goes" - in this case, "another one" ("otra" in Spanish) is feminine.
"solo otra vez" means "only one more time" in English.
in another life
Another / Other