Is it correct to say that a high variance feature will be important to my model? Analysing 3 features I was faced with the following situation:
Two of them have almost no variance and the last one have a greater variance than the other (almost two times). Is it correct to assume using only this information that the feature with more variance will be more important to my model ? Also, if a feature has 0 variance the model simply won't learn anything from it, am I right? 

Lastly, if you have some nice references I would love to read them.
High feature variance does not imply any sort of relationship to the target variable you're interested in modeling. Suppose you are looking at a population and have two variables for each person, their height in meters and annual income in dollars. The variance of height will be a small number (heights don't vary by much more than 1 meter), but the variance of income will be a large number (incomes can vary by thousands). If you want to predict the person's arm span, their height will be a much better predictor than their income, despite the fact that it has a numerically smaller variance.
A zero variance feature does not have any predictive power, but even numerically small fluctuations can be very important depending on your goal.