Japanese language is
日本語. But if I want to say
The language of Japanese people - should I write
And if I want to say the same about animals, for example
cat - like
cat's language - is it right to say
Many countries/cultural groups already have a predefined ~語 in Japanese, アラビヤ語, セルビア語, for example.
言葉 is the all-purpose word for "words" and "language" ... the kanji do it justice as "leaves of talk"
言語 actually leans more toward "linguistics" 言語学 or "the study of language"
言葉は水だ "language is liquid" or "language is water" ... I don't think it would work as well using 言語 instead.
If you wanted to ask someone what languages they speak, you could ask 何語 話せますか OR どんな言葉 話せますか