For you first bowl you did OK. 
It appears to be maple that is starting to spalt (rot). That can be difficult to get a smooth finish on because of the end grain tear out, especially around the center of the growth rings. You can usually "grind" it down by sanding starting with 80 grit paper and working your way un the grit ladder to 320 or 400. Another way to remove (most) tear out is if you can reverse you lathe direction and take light cuts with a sharp round nosed scraper. That way you are pulling the grain from the opposite direction. p