Please read the care instructions for each piece in the item description. But in general...
Microwave: Items that have 22k white or yellow gold, or mother of pearl luster, are NOT microwave safe. Most other things meant for food and drink, without lusters, are microwave safe.
Dishwasher: Items with 22k white or yellow gold, or mother of pearl luster, should be hand washed. Repeated washes in the dishwasher could lead to the lusters wearing away. All other non-lustered items are safe for the dishwasher, but if an item has delicate 3D details, exercise caution in placing your pottery in the dishwasher.
Oven use: Most pottery I sell is able to go in the oven, but I suggest heating your pottery in the oven with the preheat cycle to avoid thermal shock. To avoid thermal shock, try to let your pottery cool naturally to room temperature, or heat up gradually with the oven.