If placing the gas in lime water will turn the solution milky, then the gas is most probably carbon dioxide, the lime water (Ca(OH)₂) turns milky due to the formation of solid CaCO₃ that is insoluble after reaction with carbon dioxide.
Carbon dioxide also puts out the flame in the splint test because it does not support combustion.
Iodine is most reactive because it is very close to having a "full shell" which is 8 electrons so they are "eager" to gain the last electron to became balanced, so that makes it the most reactive. Hope that helps:)
