How firm is this topper?

It provided a firm base for a visitor with a sore back. She was very grateful .

What size is the box the mattress is shipped in?

The mattress topper comes in compressed and rolled so the box is probably almost the same size as the box for an upright vacuum. That is the closest I could think of. The mattress topper was folded in half as well so the height is the half of the width of your queen size. Hope that helps.

Does it move or slide around on top of the mattress?

Not at all. Just make sure you get the correct size - measure the bed and then look at the foam dimensions instead of relying on traditional sizing. The fitted sheet goes over both the mattress and the topper and aside from comfort you’d never know it was there as there is no movement.

Can I use this on an existing memory foam mattress?

Yes, you can.