He reached his destination, walking 3 miles (while) listening to music.
Walking 3 miles (while) listening to music, he reached his destination.
Having walked 3 miles (while) listening to music, he reached his destination.
Do the above three sentences mean the same? And here, his walking and listening to music are happening at the same time. Are all of them grammatically correct?
He reached his destination after walking 3 miles (while) listening to music.
After walking 3 miles (while) listening to music, he reached his destination.
Correct as is: Having walked 3 miles (while) listening to music, he reached his destination.
The first two are the same.
He reached his destination, walking 3 miles (while) listening to music.
Walking 3 miles (while) listening to music, he reached his destination.
The third one is just different in verb tense, and does somewhat mean the same thing, but it is using the past perfect tense.
Having walked 3 miles (while) listening to music, he reached his destination.
Using past perfect is like extending farther into the past while your sentence is already in past tense.
For instance,
We were starving and we hadn't eaten for two weeks.
Tom won the lottery, but he had already known the winning numbers.
Lassie returned. She had been missing for 8 years.