Normal distribution and Random Forest
If you use tree-based algorithms like random forests the data distribution should not be an issue. Linear algorithms are more dependent on the distribution of your variables. To check if you overfit can try to predict your training data and compare the result with test data. The score depends on your evaluation metric. If you use scikit-learn you get R^2 as your metric.

The coefficient R^2 is defined as (1 - u/v), where u is the residual
sum of squares ((y_true - y_pred) ** 2).sum() and v is the total sum
of squares ((y_true - y_true.mean()) ** 2).sum().