Also é and è: crème, café, etc. Words that originate from France, but they’re used in the Netherlands as well. We also use the accent aigu for emphasis. Also ê for maîtresse, crêpe, etc.
They've split Finland pretty arbitrarily into areas where (supposedly) Swedish speakers are found for 'å', but there's really no reason for it. The letter is a part of the Finnish alphabet and taught to everyone in school, so it should cover the whole country I think.
æ is in purely Latin words like ex æquo, et cætera, or curriculum vitæ, that's all. œ appears in œil (eye) so you see that a lot more commonly already, but I can't think of any other word that uses it off the top of my head (beside other derivated words like œillères). (pardon the puns)
Wikipedia gives examples of "curriculum vitæ" and "et cætera." We use those both as loanwords in English, but I've only seen it as the separate letters "ae," not the ligature æ.
According to German Wikipedia it is old spelling and thus, no wonder you didn't come across it:
In Italian, the circumflex used to be used primarily in the pluralisation of words with a final -io to mark the coincidence of two -ii: il principio "the principle" → i principî, in contrast to i principi, the plural of il principe "the prince". In addition to principî, there was also the full spelling principii, which was not pronounced correctly. Today, the words for "principles" and "princes" are spelt principi without distinction.
(translated using DeepL)
According to the English article, it is also used in Emilian and Friulian. In both, a long vovel is indicated with a circumflex.
But I have come across other old spellings, like "j" used in diphthongs in place of "i", like in "jeri" (old spelling for "ieri", "yesterday") or in "naja" (old word for compulsory military service time). So it must be even older/rarer than that, and I would still say "j" it's not an Italian letter because nobody uses it exept to write "Jesolo" but that's a name, not a regular word.
Fun fact: because of the old usage of "j" some text to speech are "broken". The one on railway speakers always reads "RailJet" as "Railiet" which sounds funny.
Diaereses and grave accents are used in English too, strictly speaking, just not seen very often because English typing apparatus tends to lack a way of typing them easily.
Well in french, there are no special character but variation of normal character. Except maybe for œ and æ. Also I'm curious to see an example of ÿ in use.