With tree regression, you can be a little more relaxed about assumptions. In particular, you simply give up on the "linearity" (or more precisely, the correct functional specification) assumption, because the natural process obviously does not follow the piecewise flat segmentation that is assumed by the tree model. Instead, you simply acknowledge that the model is wrong with regard to the "linearity" assumption, but proceed anyway, hoping that the flexibility and ease of interpretation of the model overcome this glaringly incorrect assumption.
The normality and constant variance assumptions have at least two useful aspects as regards tree regression. (1) The within-node prediction bounds $\hat y \pm 2 rmse$ make sense under these conditions; (2) The least squares estimation criteria also makes sense under these conditions. Absent these conditions, alternate estimation procedures and prediction bounds are better.
In your case, it is clear from the outlier-prone character of the q-q plot that you could do better my using something other than least squares. Perhaps mean absolute deviations.
It is also clear that your model will miss observations occasionally by many more standard deviations (eg, 5) than you might expect had the distributions been normal. This is not necessarily a problem; it's just good to know how your model works.