Blender Python - How to create path and folder structure from within Blender

Question

I have some experience in programming, so I know the basics of Python in Blender. I know how to dig through the Blender Python Refernce but it is very much to look around.

I know I need to import bpy and os but I am not sure how to correctly get what I want.

I know I can create a custom Panel in whatever world or Area I need:

class panel1(bpy.types.Panel):
    bl_idname = "panel.panel1"
    bl_label = "My Custom Panel"

    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "world"

# Zeichnet den Button zum Öffnen des Message Fensters
    def draw(self, context):
        layout = self.layout
        layout.row()
        layout.operator("open.browser", text = "Browser Bowser")

class OpenBrowser(bpy.types.Operator):
    bl_idname = "open.browser"
    bl_label = "Minimum code to open browser & get filepath"

    filepath = bpy.props.StringProperty(subtype="FILE_PATH") 
    #somewhere to remember the address of the file


    def execute(self, context):
        display = "filepath= "+self.filepath  
        print(display) #Prints to console  
        #Window>>>Toggle systen console

        return {'FINISHED'}

    def invoke(self, context, event): # See comments at end  [1]

        context.window_manager.fileselect_add(self) 
        #Open browser, take reference to 'self' 
        #read the path to selected file, 
        #put path in declared string type data structure self.filepath

        return {'RUNNING_MODAL'}  
        # Tells Blender to hang on for the slow user input

def register():
   bpy.utils.register_class(OpenBrowser)
   bpy.utils.register_class(panel1)

def unregister():
   bpy.utils.register_class(OpenBrowser)
   bpy.utils.unregister_class(panel1)

if __name__ == "__main__":
   register()

so the main code looks like this.

Now I want to store the path that will be selected with the browser in a var that feed/fill into a editable TextBox in the Panel that can be empty before the user select one with the browser: And I then would Need a Create Path Button, that creates SubFolder within that selected path.

like in this example:

import os

os.getcwd()
'/home/monty'

os.mkdir("foo")  #creates foo in /home/monty

os.chdir("foo") #change the current working diirectory to `foo`

os.getcwd()
'/home/monty/foo'

os.mkdir("bar")  #now `bar` is created in `/home/monty/foo`