Dealing with expressions in classical Chinese letters: 月日 and 惶恐百拜
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


  辑五瑞，择吉月日，见四岳诸牧，还瑞。


Translate into English:
Shun collected the Wurui. Then he chose a good day to meet the offcials and return the Wurui.

"五瑞(Wurui)" is a thing that offcials would like to wear in ancient. 

3)a couple of days


  伏念臣自蒙恩，改授京官，到今七年，除持服月日外，亦以四年馀两个月。——《求追赠考妣状》


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。

4)one month 


  自史太公死后，又早过了三四个月日。——《水浒传》


Translate into English：
It has been three or four months, when Shi was dead.

Old man is referred to "太公" in ancient.

5)describe time is short


  羣小无知，，故求全月日之命耳。——《魏书·王建传》


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.