It certainly should be stored cold, but served at room temp shouldn't be a problem.
The grapefruit adds a grapefruit flavor, as there is grapefruit juice and zest. I haven't substituted other citrus, as I like grapefruit, but I imagine you could use oranges (probably sweeter), or just up the lime juice and zest. The zest really gives the citrus some depth, so I always use it.
Experiment! Cooking is not a static art. A recipe is simply the starting point.