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You can use post-generated slides. Change the source of the slides in the theme settings.

The presentation page text areas accept as most HTML as WordPress allows in post contents.

You have an option to hide that in Graphics Settings.

Did you activate the child theme?

You mean as a background for the footer?

#footer2 { background: url(...); }

There’s the menu background colour field in the theme settings (Appearance > Tempera Settings) just for that

If what you see when you’re logged in is different from what you see when you’re not, you’re probably using a caching plugin.
Disable it and/or clear the cache to see the changes you make in the settings as soon as you make them (not when the plugin remembers to refresh the cached pages).

As far as I remember, WordPress does not impose a limit on the level of depth of the sub(sub…)menus.

Depending on the amount of menus items you have and still want to create, you may be reaching the limit of how many POST variables the browser can submit to a server at a time (limiting the number of menu items, either sub or non-sub, you can create/save) – WordPress menu item limit forum topic.

And Parabola supports at least 4th level submenus without problems (that’s how far we’ve tested it). You can see this in the theme demo (the “Dropdown” menu).

On small mobile devices, the menu turns into a drop-down selector.

You can test that functionality by resizing your browser window to a very narrow width (under 600px).

If the dropdown is not visible on small-windowed desktop browser, make sure you don’t have JavaScript errors in your site. If you are sure you don’t have such errors, please post a link to your site.

lacadmin, could you post a link to your site?
In what way did you “lose” the slider? How does it behave now?

Yes, it supports child themes (including many of the core functions).

The categories (blog posts) layout is controlled by the Main Layout option (in the theme settings), which applies to everything that doesn’t use a specific layout page template.

The CSS tags for customizing the main menu are listed in the theme FAQs.

This isn’t doable (without complex code changes) yet.

In WordPress, the image administration is done via the Library – Media > Library;

You could use a plugin like WP Hide Post to do this.