Well, without more precision about the problem, I would answer that I see no theoretical concern with having higher variance than mean, especially knowing they are not in the same unit so difficult to compare... Neither with having higher standard deviation than mean, by the way.

Try to partition the data and study the mean and variance of each partition. Considering the problem on hand you may devise an analysis

If the zero point has no special meaning in your application area then, like Emmanuel, I wouldn't be concerned that the mean is smaller than the standard deviation (an easier comparison). However, if it does have special meaning, e.g. positive values are valid and negative values are invalid, then you might want to apply a log transformation or the like to any variables whose negative values would be invalid.

Not sure I get your question. The answer would deped upon what trying to explain. The mena is mostly a location pararmater, while the variance is a measure of disperssion around the mean. Let us assumme that the data is Gaussian, then, if you work with the standarized variables (X-Xmena)/Xsdev, the relative values of mean and standard deviation may not as important for your analysis.