I edited the portion of your question out that asked about Othello and Iago's reaction to something that happens later. This is a separate subject, and must be asked as a separate Enotes question.
As for the musicians, I really like this question, since this part of Act III, scene i is often cut. Many producers of the play Othello are a bit confounded by the Clown, and, as a result, often chose to cut him out of the play to retain the continuity of the action. However, Shakespeare was a master dramatist and knew his audiences very well. He knew which points exactly in a tragedy required comic relief in order to lessen the tension for the audience momentarily and, simultaneously, release some of the tension through laughter. And Act III, scene i, is such a moment.
Act III, scene i is the first entrance of the Clown, and depending on how outlandishly he is costumed (and how jarringly, given the continuity of time/place of the other characters' costumes), really has potential for surprising and delighting an audience with his incongruous entrance.
But, back to Cassio and the musicians. The entrance of the musicians might not, in Shakespeare's day, have actually been an entrance at all. We are pretty certain that, during the performances at the Globe, there would have been musical interludes, presented with the same intention as the intermissions used today during theatrical performances. The musicians may have, in fact, already been onstage performing such an interlude just before Act III, scene i, and Cassio might have resumed the action of the play right out of that moment.
Cassio is a good choice of character from the play to bring the musicians to play outside Othello's residence, since such a move brings the audience right back into the circumstances of the play: Cassio is out of favor with Othello and desperately trying to get back in. So, he has hired musicians to put Othello in a good mood.
And, once Cassio has brought the musicians into the events of the play, the Clown enters to give everyone a good laugh over his "wind instrument" (fart) joke.
In answer to the second part of your question, Othello never hears the muscians, since the Clown sends them away, telling them:
If you have any music that may not be heard, to't again. . .go, vanish away!
For more on the Clown and Act III, scene i, please follow the links below.