What is the Halacha re LISTENING to someone speaking in a microphone on Shabbat. For example if I walk into a room and someone is lecturing/speaking on a microphone an I permitted to listen
According to those who maintain that microphones are prohibited on Shabbat (see, e.g., Rabbi Yisrael Rosen's thorough summary of the views, cited by @mbloch here), it should still be permitted to "eavesdrop" on the audio of a gentile speaking to a gentile audience, based on the Talmudic principle of ner l'echad ner l'meah - a lamp [lit] for one [person] may illuminate for a hundred [people] (Shabbat 122a). See, for example, the ruling of the Shulchan Arukh (OC 276:2) regarding the lighting of a lamp:
ישראל ועכו"ם שהסיבו יחד והדליק עכו"ם נר, אם רוב עכו"ם מותר להשתמש לאורו, ואם רוב ישראל או אפילו מחצה על מחצה - אסור
When a Gentile lights a candle at an assembly of Jews and gentiles; if most of those present are gentiles, one may benefit from the light of the candle. However, if most or even half of those present are Jews, it is forbidden.