In random forest, what happens if I add features that are correlated?
Random forests don't suffer from correlated variables like linear regression models do. Random forests randomly pick from a subset of variables at each split (hence the "random" in "random forests"). This means that correlated variables are less likely to show up together when the trees are being trained. But even when correlated variables show up in the same random subset of variables, it's still not much of an issue because the variables aren't assigned coefficients. 

Correlated variables are mostly an issue for linear models that try to hold all other variables constant when calculating coefficients during training. The variable selection process is much simpler for trees and tree-based algorithms like random forests and gradient boosting. When a random forest is being trained and a tree's split is being evaluated, the algorithm will simply pick whichever feature most reduces error on that particular split of the tree. Once a variable is picked, there is no coefficient, just a greater-than/less-than split point, so the problem of "exploding coefficients" doesn't apply.