Yeah, it can take some experimenting to find the right mix of humidity & ventilation that will keep the egg case from getting moldy. If you let the case dry out the mold should go away with no harm done. A jar with a mesh lid partly covered with packing tape is what I use for egg cases.
Do you have fruit fly cultures going? Drosophillia melanogaster (small) and D. heydei (large) will be needed for their first month or so until they can take on very small crickets, house flies and moths. It's good to have both sizes of fruit flies on hand incase the babies are afraid of the larger flies. If you don't have access to the flightless fruit flies in Singapore you can catch the local flying kind with just a few banana peels and some old fruit in a jar and start a culture with wild fruit flies and culture them the same as the laboratory fruit flies (you can find culture medium recipes online). With flying fruit flies/house flies you just have to remember to put the container in the freezer for a couple minutes before transferring them so they can't fly for a few minutes, just hop.
Mantids go through some sort of embryonic stage but when they emerge they are fully formed mantids - just ant sized and moving at the fastest speeds that they will ever move! Be forewarned they can end up running everywhere if you get a mass hatching. The first time I hatched a Chinese Mantis ooth and unscrewed the lid on my hatching jar I had baby mantids leaping out of the jar and running everywhere! I had no idea they would be so fast moving and with 100+ running in every direction.... It seems to be the hatchlings who are the fast movers (baby stick & leaf insects are the same way) but after they've been out a few days they calm down to their standard level of near inactivity. Once they find a spot they like they will stay there for days moving not much more than their head or to preen and groom themselves sort of like a cat does. lol