I found the second part of my question my own, sorry for any inconvenience.
1) How can I make and run a simple window with WindowBuilder?
As lakshman said,
Go to File -> New -> Other. The "select a wizard" window pops up.
Double click in WindowBuilder folder and then to Swing Designer subfolder.
Click to the Application Window and then click Next.
Give a Name for your new window and then click Finish. The Source code of the new Window pops up.
Press Run (the "Play" icon of the toolbar) to run your newly created window.
2) How can I access the WindowBuilder Core from my Eclipse and show up the toolbar with buttons and textboxes e.t.c.?
To access the core WindowBuilder you have to switch to the Design View of your newly created window. To do that, just press the Design tab at the end of the window tab. You will see the core WindowBuilder Toolbar (or "Palette") and you will be able from here to drag-n-drop the controls you want into you window.