Is it only live music that is prohibited during Sefirah or even recorded music?
Recorded music does not have the Din of music.
the rabbi didnt hold of the issur music at all during sefirah no?
Rav Yitzchak Abadi z"l was of the opinion that one should ideally refrain from listening to music year round because of the Gemara’s discussion of aveilus over the Chorban. However, that restriction on music applies specifically to music used for extra enjoyment and elevated simcha. When music is used therapeutically, to restore a person from sadness or emotional depletion back to a healthy baseline, it is not considered the same type of simcha.
At a wedding, bar mitzvah, siyum, chanukah, purim and lag baomer is live music fine?
These are all Seudot Mitzvah. No problem.