Handling outliers and Null values in Decision tree
Outliers: In decision tree learning, you do splits based on a metric that depends on the proportions of the classes on the left and right leaves after the split (for instance, Giny Impurity). If there are few outliers (which should be the case: if not, you cannot use any model), then they will not be relevant to these proportions. For this reason, decision trees are robust to outliers.

Null values: You have to replace them (unless the software you use already does that for you, which is not generally the case).

Edit about outliers:

What I have said in outliers is only about classification trees. However, it is certainly not true in regression tress. Regression tree split criterium depends on the averages of the two groups that are splitted, and, as the average is severly affected  by outliers, then the regression tree will suffer from outliers. There are two main approaches to solve this problem: either remove the outliers or build your own decision tree algorithm that makes splits based on the median instead of the average, as the median is not affected by outliers. However, basing the tree algorithm on the median will be very slow, as computing the median is way slower than computing the average.