Questions about example sentences with, and the definition and usage of "Earbuds"

A: Nothing, but "earbuds in" is more common in my experience.

"On" is usually used with headphones.

A: I believe an earbud is just something you put in your ear to block out noise, whereas you listen to music with earphones

A: Earbuds are the ones that you put in your ears to listen to music they are similar to earphones, but there is a small difference. Earphones come with cushions and earbuds don't have any cushions.
Headphones are the ones that you put on your ears to listen to music.

A: ear buds typically go in your ear while earphones go around your ear (think of gaming headsets for earphones)

A: Casi exactamente como sonaría si la trataras como una palabra en español.

A: You need something here to connect the two thoughts of the sentence. You can't just eliminate "in order".
In addition to the suggestions of Heiroglyyphics, you can say:
"I've put on my earbuds so that I don't bother her" (This is the best option, IMO)
"I've put on my earbuds so as not to bother her"

A: There is an old rule that says it is best not to split an infinitive. Most people no longer follow this rule, but many people still use it. Personally, I try not to split infinitives.
In your example, "to hear" is the infinitive, so to avoid splitting it, you should say "not to hear".
"I promised never to use that word." (not "to never use)
"On Star Trek, the explorers wanted to go boldly into space." (not "to boldly go")
That being said, splitting an infinitive is generally no longer considered incorrect. You can use either of the choices you mention.

A: Audio?

A: It's sounds natural. But I would normally say it this way personally:
"I didn't hear you because I had my earbuds in."

A: × It was the wireless earbuds that my brother gave to me, and I really like it.
✓ It was the wireless earbuds that my brother gave to me, I really liked them.

× I walked around the house trying to look for my earbuds, but they were no where to be found.
✓ I walked around the house trying to find my earbuds, but they were no where to be found.

× I went out without my earbuds for days.
✓ I went without my earbuds for days.

× Then just yesterday while I was cleaning up my room, I found them falling on the gap between my bed and the wall.
✓ Then just yesterday while I was cleaning up my room, I found them falling in the gap between my bed and the

× I was so happy and promise myself to be more organized so I don’t misplace things again.
✓ I was so happy and promised myself to be more organized so I don’t misplace things again.

A: Yes

A: It's a casual way of saying "put in."

A: #1 is correct. She feels the sounds so strongly she awestruck (like in the presence of a god). She's probably not used to city sounds or comes from the country.