Now let's begin with the syntax analyzes:
波兰(Subject) 是(Prediate) 欧洲最漂亮的(Adjective) 国家 (Object).
The whole statement is structured by:
S+P+Object. But there comes a short pharse to modify the Object:欧洲最漂亮的.
最:means "most" in English, used as an adverb to modify the adjective 漂亮 (beautiful).
And let's come to "……的", it REALLY has many usages, according to your descriptions, "最...的" is a fixed phrase, yes, that's right.
Besides, a verb/adjective + 的 = someone who is doing the job/relying on sth.
E.g:
卖鱼(selling fishes) <=> 卖鱼的 (fish-selling men).
卖花(selling flowers) <=> 卖花的 (flower-selling men).
And what's more——For MOST CASES, We add "的" at the back of an adjective to modify a noun:
漂亮 is an adjective, but we don't say:他是一个漂亮人 but 他是一个漂亮的人
Another example: 这是一个木头的船。
Sometimes "的" means "A belonging to B,part of B":
我的苹果(My apple), this apple belongs to me.
牛的眼睛(An Ox's eye), this eye belongs to the ox.