The entire bra is that soft, flexible, relatively thin foam. There are no extra pads, like how some bras have an extra pad at the bottom as a pushup. But it is on the "thick" side compared to unlined bra. This is my favorite bra :)

HanesWomen's SmoothTec ComfortFlex Fit Wirefree Bra MHG199

HanesWomen's SmoothTec ComfortFlex Fit Wirefree Bra MHG199

Q: Are there small slits or pockets to insert padding?

There is small slits but the padding is completely sewed in.

Q: The description says to hand wash, but can I wash it in my washing machine that has a "hand-wash" cycle? Can it be put in the dryer on low?

I wash mine on regular in the machine and hang dry it is fine.

Q: Smoothes back fat or makes it more ovious?

I think it smooths it a little bit. It's not the best bra I've had for back fat but definitely not the worst. As long as you buy the right size I suppose. But it is ridiculously comfortable. Hope this helps.