I still see the soul/spirit as a philosophical construct. There's no real hard evidence that we exist apart from our bodies, although we've got a lot of anecdotal evidence that some people want to accept.
And it's funny because even the ancient Jews (from which Christianity descended) had no real idea either, which is why they took desecration of the body (whether it was a criminal's body left out to be devoured by animals, or getting tattoos, or diseases which left one physically unclean, etc.) so seriously. A violation against the body is a violation against one's being, i.e., soul. Both believer and unbeliever went into the grave (Sheol) at death, and only JHVH knew what happened after that. Being executed for a crime was literally a "damnation" of sorts, since the body was being killed.
The whole abortion argument also hinges on the idea of a soul, rather than as perhaps a "developing human." Realistically, it seems that "souls" (which include body, mind, and emotions) develop from a state of no knowledge and/or efficacy from conception throughout childhood to adulthood and thus grow in power and stature and influence.
(as a side note, it makes sense to say that intrinsically all humans are 'equal' in value as human beings; but it's interesting that we sometimes decry abortion and yet permit war against civilians, if we think it necessary. In a sense, we do attribute more value to people at different stages of life.)
As far as the clone goes, I think the clone would be another body. Thus another "soul" although i consider "soul" to describe the totality of a person including their body, NOT as something abstracted and separate from it. If the brain itself had been duplicated, the person would differentiate from the time from which the cloning occurred and you would see the clone individualize based on its new experiences.
ps. no, I'm not having sex with my clone. (Talk about fubar.)