- It should NOT change color of the image.
- Brushes in Photoshop are grayscale and contain no color data. You simply cannot create a color brush. All color is chosen by the user when painting with the brush. In addition, a specific form of multi-coloring, such as green for leaves brown for trunk, is never possible in a single brush. Any multi-coloring is done in a jitter or random fashion. It is not possible control separate areas of a single brush for separate color applications.
- It should NOT rotate the tree.
- Rotation is an easy setting to apply and leave.
- It should NOT randomize size of the tree (size of the tree should be as big as the brush size).
- Not really certain what you envision. With brushes, the size of the brush is the size of what is painted, but brush sizes can be changed very easily.
In short.... Photoshop brushes aren't going to work as you are envisioning. Primarily due to the color aspect. Brushes are not an "image stamp". They are brushes, and just like real world, analog brushes, they may have different tips and can be different sizes or loaded with various colors, but they don't simply "apply" a pre-colored image like a rubber stamp.
Now, if you merely want the shape of trees, that's easily accomplished.
- Open the tree image
- Edit > Select All
- Edit > Define Brush Preset...
Then simply pick a color and paint with that brush...
You might find some benefit in exploring
Filter > Render > Tree