There a dispute between tanna kamma- torah was given on the 6th of Sivan, and r Yosi- Torah was given on the 7th of Sivan.

Certain details everyone agrees to. The Jews came to Midbar Sinai on Rosh Chodesh and the Torah was given on Shabbos. The first day the Jews came no info/laws were given bc everyone was tired from the journey. Day 2 of Sivan was the day when the Jews were told ואתם תהיו לי ממלכת כהנים. Day 3 of Sivan was establishing boundaries around the mountain. Day 4 of Sivan they were told to abstain “today and Tom” from relations before “the third day” would be matan Torah.

The rabbanan interpret this simply that there was 2 day period without relations- the 4th and 5th of Sivan- and the Torah was the 6th if Sivan on the 3rd day. Accordingly, it must be Rosh Chodesh was on Monday.

R Yosi holds Moshe added a day to “today and tomorrow.” Since “today” would be incomplete, Moshe added an additional day, so the total period of abstaining from relations was 3 days- 4, 5, and 6 of Sivan, and the Torah was given on Shabbos the 7th of Sivan. Accordingly, Rosh Chodesh was Sunday.

The Gemara quotes a braisa assuming they Jews left mitzrayim on a Thursday. Nisan is always 30 days, which means Rosh Chodesh Iyar that year was a Shabbos. Usually, iyar is 29 days, so Rosh Chodesh Sivan would be Sunday. (Like r Yosi) The rabanan say Iyar was 30 days, so Rosh Chodesh was Monday.

Moshe did 3 things acc to his own understanding and Hashem agreed- he added a day before matan Torah, separated from his wife bc Hashem was constantly speaking with him, and broke the luchos bc the Jews were doing Avoda Zara.

The Jews first received Laws of Shabbos in Mara b4 matan Torah. There’s a dispute in the gemara if they received the laws of techum at that point as well.