All perfect praise be to Allah
So, when you have concluded to it being haraam (which is right conclusion), you should treat these things as HARAAM....
Let me tell you a hadees, about something whihc is haraam on men, but not on women.
The Prophet (peace be on him) once saw a gold ring on a man's hand. He
immediately took it from him and threw it down saying, 'Does a person
pick up a piece of burning coal and hold it in his hand?' After the
Prophet (peace be on him) had left the place, someone asked the man,
'Why do you not pick it up and benefit from it?' He replied, 'No, by
Allah! I shall not pick it up after the Messenger of Allah (peace be
on him) has thrown it away.' (Reported by Muslim.)
The purpose of the above hadees is to show you the approach of sahaba and prophet towards haraam things, While musical instruments being totally haraam for all of the muslims needs to be destroyed, or at-least they must not be in your home! This is a seperate issue if we can sale them and benefit from the money of their sale, for its answer see this fatwa.
Prophet (Allah bless him) stated in a sound narration,
“Whoever leaves something for the pleasure of Allah, Allah will
compensate him with something better than it.” (Ahmad)
As believers, we only seek the pleasure of Allah since the religion is nothing but obedience and total attachment to Him and His Prophet (Allah bless him and grant him peace). Imagine the compensation of the Creator of the Worlds… it is unimaginable. Seek His pleasure sincerely and the path will be lit brighter than ever and the veils of the dunya will crumble.
Ref: Selling a Musical Instrument.
Now on second question:
It is clear i think, that we should try our best to not hear the music. If you can put some tilawat or some byaan or some nasheeds or naats in handsfree thats also fine. As long as you are not liking the music and you are trying your best to avoid that. You need not to worry, keep your prayers steady, do astagfaar as much as possible. It is not because you are sinning, prophet used to do astagfaar 70 times a day, even though he had no sins, so its always better to do astagfaar.
Allah knows best