How to unpublish a node with vocabulary term X after Y hours? How could I automatically unpublish a node after Y hours (e.g. after 24h after it appears on-line) but only when it has a specific category - category is based of course on taxonomy's vocabulary. 

Important is that an editor has no influence on number of hours after which the node is unpublished - so it must be predefined by the admin.
Use the Rules module for this, by performing these steps:


Create a Rules Component to unpublish a node, which is like a getting started with Rules Components.
Create a Rule like so:


Rules Event: After saving a new node.
Rules Conditions: check if "it has a specific category - category is based of course on taxonomy's vocabulary" (as in your question).
Rules Action: schedule the execution of the Rules Component, to be executed after 24 hours. You'll have such Rules Action available if you enabled the rules scheduler (sub-module of Rules). This will actually execute the Rules Component "next time cron runs". So make sure to take that into account also to set the frequency of your cron jobs, and/or schedule the Rules Component a bit before the 24 hours have passed (whatever fits for your case). Note that the one who can edit the rule will be able to "predefine" when the Rules Component will be executed.