The blues in Picasso's painting seem to communicate his sadness. It makes me a little sad, too.

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Q1: Do we have to use the plural form 'blues'?
Q2: What does 'It' refer to in the second sentence? Does it refer to 'The blues' or 'Picasso's painting'?

Yes, because the reference is to different shades of blue.

I'd say "it" is referring to "sadness" in the previous sentence.