How big are they? Not very. Slow steppers are about a half a millimeter long.
Where can they survive? Moss piglets are famously hardy and can survive in the vacuum of space. They can be completely dehydrated for 10 years, then rehydrated. They can survive in boiling water, the desert, the ocean, in permafrost and just about anywhere else you can think of (not lava).
Are they cute? Ehh. Under certain circumstances, sure. It’s not a cuteness home run though.
Where does one acquire a tardigrade? They are found far and wide on every continent. Your best bet for getting your hands, or microscope as it were, on one is to collect some lichen and look at it through a microscope. For the long explanation, read this very detailed article.
How do they move? They walk, much like you might imagine an 8 legged dog might.
What’s the proper care and feeding of a tardigrade? Put some agar in a dish. Water bears, as they’re sometimes called, enjoy swimming in mineral water and dining on algae. Rotate their food and water every 3 to 6 days.
When were they discovered? According to Wik, Johann August Ephraim Goeze first described what he called kleiner Wasserbär in 1773.