The saggy loose pouch is called the primordial pouch and is actually a normal part of a cat's anatomy. There is a perception that it becomes more prominent with spaying or neutering but from what I've read, this isn't actually true. It can become prominent in cats who have not been altered as well, especially in cats who are overweight, or who have recently lost weight.
All of my female cats have been spayed but I've only had one with the prominent pouch, my current cat Chula. It actually swings back and forth when she runs but is completely normal.
The lump on one side is a little more worrisome. I would have that checked out by the vet as soon as you can.