Please help me with an answer to my dilemma:
Is there a liquid that could be used to fill an ice rink (non-explosive, non-poisonous, etc), and have the freezing point above 0 Celsius?
The answer to this question is "probably not". The reason for this is quite interesting.
Ice skates have such low friction because a layer of water forms in between the ice and the blades. In order for this to happen, you need a substance that will turn from solid to liquid when it's compressed, which (according to thermodynamics) is the same thing as having a liquid that expands when it freezes. If you don't use a substance with this property then your skates are just resting on a solid surface and friction will prevent you from going anywhere.
But water is quite unusual in having this property. There are other substances that do it, but not many. The most comprehensive list I can find includes only water, silicon, gallium, antimony, bismuth and acetic acid. The metals can all be ruled out because you'd have to heat the floor up to close to their melting point. Acetic acid comes close: its melting point is $16$-$17^\circ C$, so you could in principle skate on a floor made of the stuff at only a little below room temperature. But unfortunately pure acetic acid is corrosive and has a pungent smell (it's what you can smell in vinegar, but this would be the purified version, so much more intense) so it wouldn't be suitable for a public place.
Maybe there is another molecule that has the desirable properties, but it seems kind of unlikely, because these substances are easy to spot - the solid phase floats on top of the liquid one - so if there was another one it would probably already be known.