I've been taught that if you can't make an umlaut, the the correct spelling would be with an "e". It's not difficult.
You sir, are 100% correct. Apparently web addresses don't support umlauts, so pretty much the only time you see the vowel+e format here is for websites.
What language uses ë or ï? Never saw those in German.
ë and ï I've seen in French, and apparently it's also used in Dutch, and some eastern European/west Asian languages.
Edit: oops, Eric beat me to it.
I know it seems like a pretty nit-picky thing, but if I met a Chinese guy who said "I love drinking Cars Banquet, it's my favorite beer." I'd probably tell him "Naw dog, it's spelled 'Coors.' Also, drink better beer."