I have a heat stone which functions just as heating pads. One concern is that it is heated in microwave. Sometimes I give it to my kids. One day a thought came to my mind that what kind of wave does this stone emit after being heated in a MWO? If it emits wave of 2.45GHz or something because it is heated in a MWO, is it still safe for human cells or organs? (of course the guide book says it emits infrared waves after being heated...how could I check it?)
Object which are heated in microwave ovens do not subsequently emit microwaves.
The only thing a microwave oven does is make the molecules of a substance jiggle faster, which makes the substance hotter. It is particularly good at heating water molecules because they have a large permanent electric dipole moment - so foods with high moisture content are heated more efficiently than foods which are dry.
We cannot see infrared radiation, be we can perceive it as radiated heat. It's how things are cooked in a broiler. You yourself are currently emitting infrared radiation - it's how pit vipers see their prey in the dark.
The stone is only heated by the microwave it doesn't store any radiation, only heat. In particular, when it contains water. Liquid water is heated in the microwave oven so well because the molecule has a very large permanent dipole moment which causes it to turn in the microwave field periodically so that the friction with its neighbors produces the heat. The large dipole moment is also responsible for its very large relative permittivity $\epsilon_r=81$ which is one of the highest relative permittivities of any substance. No resonance of the free molecule is important for the heating.
The microwave absorbed by water is completely transformed into heat. And water stores heat very well due to its very high specific heat. Therefore, you get only the temperature determined (blackbody) heat radiation from the heated stone which is minuscule in the microwave frequency range. The only danger for your kids is a high temperature of the heated object which can burn.
Heat is heat. A stone heated by sunlight does not shine brightly afterwards.
More in detail: when the stone is heated in the microwave oven the molecules inside are jostled around by the oscillating microwave field and the temperature goes up. After you remove it the stone molecules are vibrating more rapidly than they would at room temperature - but they do not have any "memory" of why they are in that state. They will emit normal blackbody radiation (mostly in IR for reasonable temperatures) or conduct their heat by touch.
(Why is there no "memory"? Because the molecular motions quickly thermalize - they randomize each other. In other systems like phosphorescent paint the extra energy gets put into high energy states that decay in a way that releases only particular wavelengths. But this does not happen here.)