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.
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.