Right-click context menu is wrong

I'm a new user having just installed the latest demo. When I right-click on my "menus" the context menu is the normal non-TLB right-click context menu with the TLB context menu stuck at the bottom. How do I get rid of the non-TLB right-click context menu?

You can select the context menu template in the TLB Settings->Context menu
The template with TLB items only is "Without Shell/Button"

I'd also like to know how to remove a "menu". I found the FAQ kind of confusing. To me it indicated that it was OK and not OK to use the Delete key. I created a Programs menu and now I want to get rid of it.

You can delete the created Programs menu - it is safe when using the "Delete" menu item with red icon. If you deleted something inside the Programs menu, you will delete the real file/folder.

I also found that adding a menu to TLB adds it to the Quick Launch toolbar. For instance, when I created the Programs menu, it added it to the Quick Launch toolbar. When I try to delete it from within TLB, I'm told it's a system folder and can't be deleted. If I switch the QL toolbar back on, I can delete it there.

Is all of the interaction with the Quick Launch toolbar also in the stand alone version. It seems to me that I'm playing with fire by messing around with the QL toobar through another toolbar.

Yes, TLB store all shortcuts in the toolbar folder. By default this folder is same as Quick Launch uses. You can switch TLB to other folder:
Create new toolbars here TLB Settings->Toolbars, then right-click TLB select Switch Toolbar menu item and select new toolbar.