I gather you are using 1.6 (maybe 1.7 now), so I will tailor my answers accordingly...
When you have a clean 1.6 or higher install, there are a couple of modules assigned to module positions for the default template (mainmenu on position-7, etc.). Now you install a new template on Joomla!. That template will have its own custom module positions. position-7 will most likely not exist on that template, so these modules will not be shown until you assign them manually to the module positions that exist within your newly installed template. It may be that mainmenu should be shown in position header-a, but YOU will have to do the assigning part.
Hope that makes sense
Next issue: in 1.6 and higher, you only have categories, no more sections and categories. There is no need to create subcategories within categories unless you really need to.
You can create a menu, put nothing in it and already assign it to a module position on your template. It will not show much, but yes, you can... Normally what you do is:
- create a menu
- add the menu items you already want
- assign the menu to a module position
- publish the module
In your case, create your categories, then create menu items to the category blog or list layout for these categories.
If you need more clarification, please let me know!