See http://i3.photobucket.com/albums/y100/jcdenton1558/geralt_zps9a5eb842.png...I've searched and not found a solution (though I don't entirely know what to search for), just a lot of stuff about texture seams (not sure if that's the same issue, but I don't think so).

There's an unsightly gap between head and body. Is there an easy way to fix this? If not, is there any way to fix this? I'm not sure where to begin.

I can't say for certain, but It looks like a bone-weighting problem to me. The edges of the head's neckseam and the edges of the shoulder's neckseam should be weighted the same and to the same bones (I think they are weighted 100% to only the head bone if I remember correctly.)