Which non-English Morse characters are the most important ones?
The Morse code for the 26 letters of the English language and the digits, you can find everywhere, e.g. here on Wikipedia. All one-, two-, and three-symbol combinations are in use.
In the international alphabet all but four of the four-symbol combinations are used. They are:
The two or three first German letters are used in many other languages also, e.g. Swedish, Finnish, Turkish, Hungarian etc.
All other characters use five symbols. These are the ones that I have been able to find:
|-··-·||–||Ê (also /)||–||–||–||–|
There are also six-symbol combinations in Polish: Ź which is –⋅⋅-⋅ (ZN) and Ś which is ⋅⋅⋅-⋅⋅⋅ (SB). The German Wikipedia even lists a Morse code for the double S: ß, ⋅⋅⋅–⋅⋅ or SZ, but I believe two consecutive S’s work well or even better.
I recently asked on the Elecraft list if the K3 Morse decoder could support some of these letters, and I asked specifically about Ä/Æ, Ö/Ø, Å, and Ü. These are the four which are shown in the first figure in the upper right-hand corner of this post.