Three colors down the left edge: green is yes, yellow is yes with a condition, and terracotta is no. The condition is nearly always the same one, which is that water has found its way into the clay body.
Dishwasher
UsuallyA fully vitrified, uncrazed glazed piece survives a dishwasher indefinitely. Two things do not: a crazed glaze, which lets water into the body and drives the staining, and gold or luster, which comes straight off. The unglazed foot also stays damp longer than the rest, so it wants to face up.
Microwave
UsuallyFired clay and glaze are not metal, so they do not arc and they heat the food rather than themselves. Anything with gold, platinum or luster on it is metal and will spark. A thick mug still gets hot, because the drink inside it heats the wall.
Oven
Only if it was made for itThermal shock is about sudden change, not absolute temperature, so what cracks a dish is going from a cold counter into a hot oven. Put it in cold, let it come up with the oven, and never set it on a wet surface coming out. A piece with a very thick base or an abrupt change in wall thickness is the one that goes.
Stovetop
NoA burner heats one small area of the base far faster than the rest of the piece can follow. Flameware exists and is made from a completely different clay body. Studio stoneware is not it.
Freezer
If it is uncrazedWater sitting inside a crazed glaze or a porous body expands as it freezes and splits the wall from the inside. A fully vitrified piece with a sound glaze is fine.
Outside through winter
RarelySame physics as the freezer, repeated every night for four months. A garden pot cracks in the first hard frost rather than in summer, and it cracks from the inside out. Bring anything you care about in.
Food and drink
Ask about the glazeA glaze is safe for food when it is fully melted, fits the clay without crazing, and carries no soluble metals. Manufacturers test and state it. Claiming it yourself is a bigger commitment than most people realize.
Plants
Yes, with drainageThink about the hole before you make the pot, not after. No hole means gravel in the bottom and careful watering. Unglazed stoneware breathes a little, terracotta breathes a lot, and a fully glazed pot breathes not at all.
Candles
YesA ceramic holder is one of the safest things to put a candle in, as long as the flame is not directly against a thin wall for hours. Wax comes out with hot water and patience.
The bottom of a wooden table
Not without helpAn unglazed foot is essentially fine sandpaper. Rub it smooth with a stone or wet sandpaper, and put felt or silicone pads on anything that lives on furniture.