The body is limited in time whereas the soul/spirit is not. when Paul died he went in spirit to Heaven, to await the great departure coming soon. Do a bit of searching and you will find that Paul wrote that if there is a physical body there is a spirit body.
You can’t be asleep and being busy in Heaven at the same time. That’s holding two competing thought simultaneously and making them a single thought.
Yes, Paul went to the third Heaven, in a vision. Just like Moses was not actually transported to the beginning of Earth’s creation and hung in space for 7 days as God created everything. They were both in vision and writing down what they saw.