One, cold spells wont harm them - it can actually help them! On the East coast of the US, the lower temperatures slow the other insects down, enabling the mantis to gorge itself on prey that is too slow to get out of the way. It is at this time, that the adult female gets the energy needed to make the ootheca.
Food size - Yes, live food will get their attention, but they can be trained to take dead insects. Prey of one third to one half their body length can be taken. Care should be taken not to leave them alone with their prey! A cricket can kill a mantis if it isn't eaten.
If you take care of it, feild plankton, or wild caught insects, will be too much trouble. Crickets, waxworms (for a treat, let them pupate into the moth - ooh! they love them!), or mealworms of the tenebrio genus will work. Mealworms require a little encouragement though.
Once you feed it captive bred insects, you are OBLIGATED to never release it! Why? There are illnesses that exist only in captive bred insects, that could harm wild ones. In general, you catch, you keep! Euthanasia by putting in a paper bag, and putting in the ice box, should be performed if you can't care for it any longer.