WordPress set up. Can's and Cant do's

I am setting up a blog and have now figured out it may be better to see if a standard single install on the domain can do as I would like. Still considering subdomains but open to all options and opinions.

On a standard install of wordpress can I do the following somehow?

1/ Have a home page which only shows main categories and pages?
2/ have a number of subcategories which are only shown when the main category is selected?
3/ Change the header as to which category is selected?
4/ Show sidebar contents based on selected category selected?

In all, I am trying to force a single wordpress install to act something like subdomains where I can change the header image, have different categories and sidebar contents based on which category I am viewing.

Is it possible to do things like this or am I better of using subdomains? And which version of wordpress does anyone recommend I use for taking this kind of approach?

Trying to get things right from the start so I don’t have to change it all later!

Thanks for your help in advance.