Why there is an E after the U in Robt Muellers name

[Emrys]

9. I disagree with two specific points in your guide, concerning o umlaut and a umlaut u, and a few other general points

You wrote:

German Ostlich (easterly) rhymes close with toast lick. OL (oil) close with sole.

No. Östlich is pronounced more like (clumsy attempts at non-IPA phonetic explanations ahead) erstlich (don't roll the r) or uhstlich; Öl is pronounced to rhyme with earl (again don't roll the r) or uhl.

You wrote:

The umlauted au is most famous in the German 'fraulein' where the umlauted au sound is like English ow, so close to Frow line - not froy line as some do. Fraulein is also a young lady.

No. Fräulein is definitely pronounced froyline. Without the umlaut, the au combination would sound like ow, as in the German word Maus (English mouse).

In medieval times (way before the timescale you mentioned), when the orthography (way of writing) of German was still evolving more quickly than it is nowadays, scribes used to write a superscript e after the vowel they wanted to modify. Over time, this developed into the umlauted letter forms as we know them. If a certain font nowadays doesn't include the umlauted versions, using, say, oe for ö is an alternative in German, though it can look a bit archaic.

In English nowadays, in the absence of the umlauted forms, the guidance is more often to substitute the un-umlauted form of the letter, though this can grate on anyone who knows German.

Other than that, listen to Igel.