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.
I wouldn't completely rule out a gallium rink. Gallium melts at 29.76 °C (85.57 °F), which is not a terribly uncomfortable temperature when resting. The problem, of course, is that skating can be strenuous, so the air would have to be cooled, not the surface, However, it's surely cheaper to cool air somewhat than to cool water to below its freezing point, and if the air outside were cool, that could substitute for air conditioning. Besides, it's quite likely that some gallium alloy could be found that would lower the melting point somewhat, while preserving the property of melting under pressure. Also, I understand that gallium is thought to be very or fairly nontoxic; I suspect that it may also be much less volatile than acetic acid near its melting point. Bismuth, at least, might be a suitable nontoxic alloy metal. (It surely is very nontoxic, since it's in Pepto-Bismol.) Of course, even a very small toxicity could make a gallium rink illegal in most countries. There are other considerations as well, such as the viscosity of liquid gallium near its melting point. I have no research to provide; I am a mathematician and computer scientist, not a physicist.
Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.
Would you like to answer one of these unanswered questions instead?