I read somewhere that if your chrysalis is not near a plant, it will not be getting the humidity it will usually get, so spraying the chrysalises every now and then with water can stop them dehydrating.
I do actually prefer to have them hanging, I have tried the method of having them lying in a container with mesh (I used a chux cloth) and while many were fine, I did find a few of them failed to exit the chrysalis properly, as instead of it being fixed so they could pull out of it easily, it was dragged behind them, and was tangled up around the abdomen somewhat, and was quite difficult to release. The butterflies were otherwise quite fine.
Maximum sun, Katie. And warmth – if it’s comfortable for you (people) then it’s good for the pupae.
They don’t need to be hanging – so long as they can climb up something immediately their chrysalis opens. I put mine in a little net box, so they can climb up the side of the net and dry their wings. A friend puts hers at the bottom of a net “curtain” which is pegged to a chair. I have also put them on the inside rim of one of those umbrella type food covers and that worked well. Each day I check them and make sure anything that is colouring up is right next to the rim – so the butterflies emerge and immediately climb up the inside of the net to dry their wings. It works very well.
Hope that helps.