Are there standard translations for phrases like 月日 and 惶恐百拜, used in correspondence in premodern times? 'A day of a month' and 'I cower fearfully and bow a hundred times' don't really...y'know...WORK in English... -_-;
月日 may have different meanings in different context. I guess it just means date.
The literal meaning of 惶恐百拜 is I bow down to your repeatedly with full of fear, but it is just a way to show the respect and submission to someone has a higher rank such as the emperor, your boss or your teacher.
However, different meanings in different contexts.
According to Baidu Baike，there are four meanings about "月日". But in my opinion, it would be explained in five ways.
1)moon and son It is understood easily and Literally.
2)the day you choose
Translate into English: Shun collected the Wurui. Then he chose a good day to meet the offcials and return the Wurui.
3)a couple of days
Translate into English： Under grace, I have appointed as government official for seven years now. Apart from the time of observe mourning, there are four years and two months。
Translate into English： It has been three or four months, when Shi was dead.
5)describe time is short
Translate into English: We are weak, and afraid that we will be killed like the people of Canhepo. So we just want to save our short lifes.
Speaking of "惶恐百拜", the phrase was usually divided into two phrases "惶恐" and "百拜", and was used to show your respect for recipient in letter. You can check this article 《上海图书馆藏明代尺牍》书信用语研究, and also could find "顿首百拜" in many questions.
"惶恐" shows you feel anxious because you afraid of disturbing the recipient.
"百拜" doesn't mean "bow a hundred times" anyway. It looks like "Yours sincerely" and "Best regards" in letter in English. It shows your respect for recipient in the end of the letter.