1 – Is it true that in the past the Shofar was played in all Rosh Chodesh? Do you have sources for this practice dear Rabbi?
2 – Why not blow shofar nowadays at all Rosh Chodesh?
What you are writing is correct. In the time of the Bais Hamikdash they used to blow with trumpets when the Rosh Chodesh Sacrifice or when the special sacrifice for Yom Tov was brought. This is written in Tractate Succah 53b, and is based on the verse “וביום שמחתכם ובמועדיכם ובראשי חדשיכם ותקעתם בחצוצרות”‘. Nowadays we don’t blow the shofar because we are not actually bringing the sacrifice. God willing, we will merit to see the rebuilding of the Bais Hamikdash and we will once again hear the blowing of the trumpets when they will bring these sacrifices.