According to reincarnation, the number of souls stay the same, however the human population keeps growing everyday. It has even quadrupled at certain times. Where do these souls come from?
Umm no, nobody said that. New souls are created all the time. As there has been said on previous posts, not everyone is an old soul, some people only have 1 past life or zero past lives and it's their first life. There are older souls which have hundreds or thousands of lives and younger souls.
You're confusing that with the Buddhist/Hindu version of reincarnation which says humans always have reincarnated forever. Nobody who isn't a Hindu or Buddhist but believes in reincarnation accepts that. There's talk about old and young souls all the time all over the internet.
From the genetic, racial and spiritual templates of their parents and family. They incarnate as a more 'perfect' blend of these, being created completely anew.