Photoshop Creative

Is the ability to create custom shapes present in PSE6 -- that can be used with cookie cutter too?

The first answer seems to be: no...
However you can combine different custom shapes within Elements. You could save them in psd format.
In Richard Lynch's book 'The hidden power of Adobe Photoshop Elements", you have a chapter on how to create custom shapes with his tools. This is possible, but I would be unable to do it without the help of the book...
Probably not for everyday use, but designing a logo is possible.

I forgot... Welcome on this forum!

I've no idea how you'd make new custom shapes in PSE or PS, but there are lots of free extra shapes around the web so, logically, there must be a way to make them or there wouldn't be anywhere on the web to get them except through Adobe.

There's a big collection to be found at Sue Chastain's site http://graphicssoft.about.com/od/photoshopdownloads/ss/shapes1.htm.
So there's just about got to be what you want there. Don't forget that each .csh file is actually a collection of shapes, and the files go into the Presets/Custom Shapes folder.

If you go to the shapes box and click on the double arrowhead >> at the top you'll find a lot of ready-made custom shapes and, as they can all be transformed/sized/coloured I can't see a need for that many more, unless somebody required a very specialized collection, like geometric shapes, animals and fish, maybe sports. (ooo there's a good idea!)