My Air made a loud noise, I don't know, why. Can I get rid of any noises, or do I still need to listen to them for any reasons?

You'd have to explain what you mean when you say "My Air made a loud noise, I don't know, why. Can I get rid of any noises, or do I still need to listen to them for any reasons?" -- that doesn't really tell me anything.

It was like some sort of short music, 1-2 seconds, quite loud. Similar to stratup chimney, I mean, it's also like a music. Do I need these type of sounds, seems like they are some kid of notifications, as much as I understand.

I have no idea what that sound would be -- if you think it's a notification sound, I guess you should check System Preferences > Notifications.

I have sounds if I delete something from bin or if I remove something from dock. I don't want them. How can I get rid of those unwanted sounds?

You can go to Apple menu > System Preferences > Sound > Sound Effects and turn off "Play user interface sound effects". But keep in mind this will turn off ALL alert sounds, including other ones you might want/need. Alternatively you could just turn down the level of all sound effects [lower Alert Volume] to make them less intrusive, or you could select a different alert sound.