Hello,
Let’s say I run a site about mobile gadgets so I have pages dedicated to various models of smartphones, tablets, laptops.
Can I somehow group all the pages dedicated to the various models of tablets into one category “tablets” and see the collective stats for all the various pages about tablets?
One way might be to create a custom report and add rules for each page, but that would be too much work for all the pages I have.
What you could do is set up a “sement” - look for the button next to the date-picker where it says “all visits”, click that and add a new segment for each of your categories.
You can define which URIs shall be tracked as part of the “tablets” segment (p.e.) and check the different categories by comapring the different segments. You just need to tell PIWIK how to distinguish which page belongs to which category, and there are several options to do that, have a look 
So I suppose the custom variables would be the way to go - add them programmatically to the Piwik code inside all pages?
Nope, look under “actions” when creating a segment, theres page name & URI at the bottom of the list. No custom variable needed.
If the categories can in no way be extracted from page name or URI, you’ll have to go the custom variable way.