Your Adventist friend is mistaken. The Bible speaks of death as sleep because the body looks as if it’s asleep when we die, not because the soul becomes unconscious.
In the first passage you listed, Acts 7:59-60, Stephen, before "falling asleep" in death, cries out, "Lord Jesus, receive my spirit." That this doesn’t support "soul sleep" is clear from Jesus’ similar remark on the cross (Lk 23:46), which didn’t preclude his telling the Good Thief who died with him, "Today you will be with me in paradise" (Lk 23:43).
If, as the Adventists believe, human beings don’t possess an immaterial spirit which continues after the death of the body, then Stephen’s outcry (as well as Christ’s) is meaningless--there would be no spirit of Stephen for the Lord to receive.
The Bible doesn’t teach the concept of "soul sleep." Jesus’ parable of Lazarus and the rich man, for example, demonstrates that after death both the righteous and the unrighteous are aware of their fates (Lk 16:19-31).
The apostle Paul also teaches conscious existence after death. He speaks of his desire to depart this life and to go on to be with Christ (Phil 1:23). In 2 Corinthians 12:3-4, Paul tells of his being caught up to paradise and of his uncertainty whether this occurred "in the body or out of the body"--certainly an odd way of speaking if he didn’t believe in an immaterial soul or if he believed in "soul sleep."