Hi Yuki,
1. There is indeed only one brush. You can probably add more brushes yourself, but I don’t know how to do that.
2. You can save the UV’s when you enable the Addon ‘Import-Export: UV Layout’.
Then with your Object in Edit Mode (or just switch to the UV Editing Workspace):

This will save the UV’s as PNG with Alpha background. Any painting done in Blender has to be saved as Image separately.
You can set the path to your painting application in your Preferences

and then you can open your image directly in your favorite application:

Maybe some else knows a way to get the image with the UV’s in an external application in one go…