Why doesn't/does the slider load on those pages which I want/don't want it to load?
The sliders load into the module positions, what you have selected in your Module Manager, and where your website loads those module positions, that is where the sliders will show up.
Modules can only be assigned to menu items. Only these menu items are unique pages from the point of view for a module.
Beside the modules there are the contents, it is the "middle part", like the articles, contents created by webshops. In the template's code these are called in differently, seperately from the modules, and if they are called in, they can be on any menu items' pages.
If these contents don't have any menu items (= seperate pages), they can be still shown on a "not unique page", which is usually the homepage with this extra content.
This is where Joomla is using Itemid. That identifies the pages, but at the modules, you can't select from itemids, only from the menu items, which is very limited, if you think about how many possible pages you actually have on your website, but they aren't used. If you want to know, for some reasons, your itemid, you can see it in your page's url, if you turn off the SEF urls.
So this is why you can see your homepage slider in some other pages, or you can't assign your slider to a page. What you could do is to either create a new Joomla menu, and put a menu item in it, that is linking to your content
and at your slider's module → Menu Assignment choose if you want to have that module load in that page or not, or you could try out the Advanced Module Manager extension, which offers more options, where you can make your modules show up.