When does the baby gain a spirit of its own?
You could say it has always had a spirit. Sounds too metaphysical right?
Who knows when exactly, it happens at some stage during development, probably different times for different babies.
Just because mine is projected, will the baby's be disturbed?
Your very mood affects the unborn baby. You are as close to the baby as any two beings can be. Obviously, the possibility is there that you will affect the baby in some way.