For a regime proclaiming ethnic and genetic superiority, why wouldn't the German government and armed forces use German to communicate? Why use a language of a country you've declared war against? Are there any accounts of officials advocating against English in favor of German?
Was this to bridge the language gap with the Japanese and Italians? Did either of them have issue with using English?
German uses the same alphabet as English with the addition of four letters (ä, ö, ü, and the 'sharp s' or eszett, ß). Note the layout of the top line of the keyboard is QWERTZ rather than QWERTY, a layout used in languages such as German where 'Z' is much more commonly used than 'Y'. Enigma messages spelled numbers out in full, had no spaces (words were delimited with 'X'), and did not use punctuation, so the 'P' and 'L' keys were relocated to the bottom row to save space, otherwise it's a fairly standard keyboard (see e.g. a Swiss typewriter). When encoding messages, letters with umlauts had an 'e' appended ('ä' was typed as 'ae', 'ö' as 'oe' and 'ü' as 'ue'), and an eszett was typed as 'ss' or 'sz'.
There's a project to break original Enigma messages with some examples on their site, e.g. a Luftwaffe activity report. It's set out very nicely with the various stages of decryption, showing that even after breaking a message the 'plain' text is a solid string of characters:
TAETIGKEITSBIRICHTVOMXSEQSXOREIXVIERNULLXAQTXAUFGENOMMENXNULLXMEFOERDERTXLEITSTELLEWARXKRAKAUXLXGXKDOXROEMXAQTX
Fully separated and formatted, that becomes:
Tätigkeitsbericht vom 6.3.40: Acht aufgenommen, null befördert. Leitstelle war Krakau. L.G.Kdo. VIII.
(Note the 'AE' used for 'ä' in the first word, and various abbreviations such as 'SEQS' for sechs and 'AQT' for acht, 6 and 8 respectively.)
