By assassin bugs you mean white spotted or red spotted assassin bugs (Platymeris sp.) right?
1) For their enclosure I would use a shoe box with about 2 inches of coconut fiber along with peaces of cork or bark for them to claim up. Always keep substrate moist or eggs will not hatch.
2) If you have a female she doesn't need a mate. Just like a stick insects they can reproduce by parthenogenesis.
3) Expect at least 1-3 eggs per day.