Updated: Dec 16, 2019
God's calendar works differently than ours. There are roughly 360 days in His year and the months do not have names. They are simply called 1st, 2nd, 3rd etc. The Jewish names for the months used today came into usage after the exile in Babylon. They are Babylonian names. Therefore, when you read in the Bible you will see phrases such as, "in the first month". In the books of Daniel and those after the exile, one will find the current Jewish names for the months used, (Tishri, Tammuz, Kislev etc) because this was after the Babylonian captivity. The only month that God named anything more than a numbering system was the first month of the year which He called "Aviv". Aviv was not so much a name as it was a representation. Aviv means ripening and the barley was aviv in the first month.
Months were historically called by the citing of the crescent new moon.
Likewise, God did not name the days of the week. They were also called 1st, 2nd etc. The only day that was called any different was the 7th day which was called the Sabbath, meaning rest.
Days are 24 hour periods but they go from sunset to sunset, not midnight to midnight. One can see this in the first chapter of Genesis.