1) Are you allowed to listen to Music on Rosh Chodesh Iyar? 1a) Does your individual Sefirah status matter such as the first half, second half or both?
The Shulchan Aruch writes (OC 493:3) that those who think that Rosh Chodesh Iyar serves as an exception to the customary mourning practics are mistaken. (That is not a terminology he uses very often.)
Thus, if your "half" of mourning includes Rosh Chodesh Iyar, you should continue your mourning practices on that day.
Rosh Chodesh Iyar is definitely part of the mourning period, whichever "half" of sefirah one observes. One may only listen to music as part of a seudas mitzvah, such as a Sheva Berachos for a couple that got married at the end of Nissan.
The yesod is 33 days of aveilus overall.