Nah, store them any way you like. If you're a MVS guy get shockboxes, dust and moisture are the enemies of MVS games. If you're an AES guy, you're good to go.
No worries about warping thoug; hell I'd be a LOT more worried about getting boots (ebay=the place to find boots).
Nope. The PCBs inside the carts are way too small to be warped by gravity. This only happens to much bigger boards and could be prevented if more PCB feet were used to support them.