"They eat a lot of fish and rice in Japan."
Translation:Ils mangent beaucoup de poissons et de riz au Japon.
Because it is uncountable "riz" is singular and "poissons" is plural.
But, even if both of them were plural you can't say that. You can only do this "trick" of one word which concerns many words with adjectives (so in your example "la casquette et le maillot foncés" it's ok) but not with the other words. So no, you can't say "ils mangent des poissons et haricots", it's a mistake.
Moreover, with "beaucoup" you can't use "des". It's strange but when you use "beaucoup", the words "des", "du", "de l' ", "de la" become "de" :
"Il mange du poisson" but "il mange beaucoup de poissons"
"Il mange des haricots" but "il mange beaucoup de haricots"
"Il mange de la salade" but "il mange beaucoup de salade"....
So "ils mangent beaucoup des poissons" is a mistake too.
One final thing (which is not totally a mistake). Take care because if they look similar "ils mangent du poisson" and "ils mangent des poissons" don't mean the same. The first one means they eat some fish, you don't know how much and the second ones means that they eat fishes and you can count the number of fishes they eat.
I think that all the languages seem strange when you are used to yours^^
I had (and still have) some problems in English too...
But it's also true that in French we have a lot of tiny rules which don't have any sens, which may be contradicted by some others and then it may look really random^^