"Are the workers happy or sad?"

Translation: A munkások boldogok vagy szomorúak?

[VojaJ.]

Is "dolgozók" an option here instead of munkások?

[Findil]

It's a correct translation.

[NiclasLang]

What's the rule for plural or singular adjectives?

[RyagonIV]

You need plural adjectives if the subject is plural, too, and if it's a sentence of the form "[Subjects] are [adjective]", a so-called "copula sentence".
In all other cases, most importantly those with "[adjective] [Subject]" (like "the red car"), the adjectives are inserted in their base form, regardless of case or number of the noun. Let's try it:

• az autó piros - the car is red
• az autók pirosak - the cars are red
• a piros autó - the red car
• a piros autók - the red cars

[lok194322]

Why here it was "szomorúak" instead of "szomorúk"?

[RyagonIV]

Adjectives prefer using -ak/-ek as plural suffix. For instance you have idősek (instead of "idősök"), szörnyűek (instead of "szörnyűk"), or férfiak (instead of "férfik"; yes it's an adjective, too).