1) It's a typo, yes. Thanks!
2) Well, they are lossy in the sense that pronunciation is context-sensitive. The number of cases where you actually turn the word into another word is very small: http://snowball.tartarus.org/algorithms/german2/stemmer.html has a discussion.
3) You are right, I'm wrong. ß, ä, ö, ü are considered part of the alphabet. It's not tought in school, though (at least not in mine).
Thanks a lot for making the effort and fact-checking better then I did there :).
1) To avoid confusing readers that don't know German or are used to umlauts: The correct transcription is base-vowel+e (i.e. ö turns to oe - the example given is therefor wrong. Probably just a typo, but still)
2) These transcriptions are lossy. If you see 'oe' in a word, you cannot (always) pronounce it as umlaut. The second e just might indicate that the o in oe is long.
3) ß is a character in the alphabet, as far as I'm aware and as far as the mighty Wikipedia is concerned, as I pointed out above. If you have better sources that claim something else, please share those (I .. am a native speaker, but no language expert. So I'm genuinely curious why you'd think that this letter isn't part of the alphabet).
Fun fact: I once had to revise all the documentation for a project, because the (huge, state-owned) Swiss customer refused perfectly valid German, stating "We don't have that letter here, we don't use it: Remove it".