Those stems look dead to me. Cut off the green - still alive - sections; make sure there is no rot (probably not, looks like stems dried up - but not sure looking at the photos). Let callus for a while, maybe an hour, then stick into well draining mix. Put in well lit spot, not into full sun right away, and let it be for a while - they should start growing roots. Eventually, they will need better light than is getting now, but move them slowly otherwise they will burn.

That pot is huge, totally not needed for few cuttings. (If you use it for some other plants, put a bigger saucer under the pot, one you have is very tight-fitting and could have water sitting in it without you knowing.) Get some small pots, even plastic, and stick few pieces in each. These are recent cuttings:

That very long piece could be cut into few sections.

...and the fallen individual leaves, if they come detached, can be poked lightly in the soil on their own as they freely sprout new roots and plantlets.

Gill

As Rina said, well draining mix. You can buy commercial cactus mix and do 50/50 with some perlite or pumice. Another option is chicken grit.