As your belly grows with baby, there is a thin strip of connective tissue between your rectus (six-pack) muscles that stretches out.  After pregnancy, it is sometimes difficult for that fascial strip to tighten up again.  This is called RECTUS DIASTASIS, and it is the most common reason that women have bulgy bellies after pregnancy.  It can be fixed during an abdominoplasty (tummy tuck) by sewing the muscles back together (RECTUS PLICATION). 

The skin on your belly has to stretch a lot to accommodate that little bundle of joy.  Some of that stretched skin can shrink back down, but some of it stays behind.  This can result in a belly that looks fine in clothes, but looks like a wrinkly alien out of clothes.  If this is you, a skin-only tummy tuck might be the answer. 

An "outie" belly button usually signifies an umbilical hernia.  If the hernia is small, it can be fixed with stitches through a tiny cut below your belly button.  If it's very large, you may require a mesh repair.  This operation can be done alone or in combination with a tummy tuck.

C-section scars that are tethered to the deeper tissues can pull inward and make the skin above fall on top like a shelf.  This can be corrected by revising your scar, releasing the deep tether, and laying the skin back down flat. 

This question doesn't have a straightforward anatomic answer.  Many women will find that after 1, 2, or more pregnancies, they can't get their weight down where it was before pregnancy.  While the belly outpouching, excess skin, and belly button weirdness can be addressed surgically, there isn't an operation designed to get rid of an extra few pounds.  The reality is that most people retain extra weight as they get older.  Your metabolism slows down and it takes more effort to get the same results.  Add to that the overwhelming time commitment of child rearing that makes it harder and harder to exercise, eat right, and make your body a priority, and you have a recipe for excess weight that stays put.