One man's trash is another one's treasure

It dispenses medicine in tiny bits. Or t looses certan letters from ts mtts.

Round and round I go Where will I stop? Nobody knows. Sometimes I have horses and carriages, Other times mythological beasts or you feel like you've gone to the zoo.

From rooftops I may often hang, silent, cold, and sharp as a fang. Though made of water, I feel like stone, In winter’s grasp I’ve slowly grown.

One is swirled by a scientist in a lab, One's swigged from when things get bad, One keeps hot things hot and cool things cool, Handy for taking soup to work or school If you want to win this game, Figure out these three things that share the same name