> What burns hotter - white gas or alcohol?
Depends on the alcohol, but generally the answer you're looking for is White gas. [Technically, the oxidation of carbon gives off the same energy no matter what the starting reaction is, but the OH group in alcohol, plus the ever-present water content causes some of the radiant heat to be used in different ways other than light and heat]

> If I was using thin rope snakes (1/4 inch) and spinning them, what fuel would give the ropes a flame that would more likley be seen by an audience while being spun.
Also depends on the setting and the material in the rope. Pure kevlar does not like alcohol and will often go out rather than stay lit. Most times alcohol cannot be seen in well-lit situations. So, for any synthetic wicks in anything but near pitch black.... white gas, hands down.

> If I dipped that same rope snake in a fuel and lit the end, what fuel would have the fastest travel time up the rope?
The fuel with the lowest flash point. In most cases, that's white gas, but very pure versions of alcohol have lower flash points than white.