Translation:I still have not replied to your email. Sorry!
I wrote "I haven't yet replied to your email. Sorry!" As expected, it was rejected. I reported it. I hope they take it into consideration. It's getting really ridiculous!
Yes. Here it's short for 回复 （reply to）and take note that it is not return in the sense of returning something to someone （还）.
Ive never heard anyone say 电子邮件。Its most commonly either 邮件 or 伊妹儿 in my experience
"Reply" is intransitive in this sense, taking an indirect object. You have to reply to a message, in English.
You can also use "reply" like "say", for quoting direct speech, in which case you can say something like "He replied 'no'", but I would say it's more often used with "that", for so-called reported speech: "he replied that he wasn't interested".