Here the word "himself" refers to Paul. The first word "he" refers to Paul; the second word "he" refers to the young man, Eutychus. The word "him" refers to Eutychus.
This speaks about sleep as if it were a deep hole into which a person could fall. AT: "who slept soundly" or "who became more and more tired until finally he was sleeping soundly" (See: [[rc://en/ta/man/translate/figs-metaphor]])
When they went down to check his condition, they saw he was dead. This can be stated in active form. AT: "third story; and when they went to pick him up, they found that he was dead" (See: [[rc://en/ta/man/translate/figs-activepassive]])