Mine have dug a hole under the breeding net, which I have put under water and in the corner so I don't kill the gammarus shrimp breeding in it. I thought it would make a large cage with the java moss in it, which I hope will eventually cover the sides. My crayfish dug a tunnel under the net and use it as a cave.
My thoughts on your missing crayfish -- if your betta killed it, likely it was right after it molted. Otherwise, it dug a cave in the substrate and hid really well after molting.
For food, I've been feeding a variety of defrosted food, betta pellets, and algae wafers. I do the same with my shrimp and the assassin snail. Once I push a pellet down with my finger, it usually sinks to the bottom (or gets shoved around by the filter for a while and caught on a plant, depending on the tank).
10 gallons, petco king and community fish
1 x 5.5 gallons with shrimp and plants
1 x 5.5 male veil tail with plants