Sometimes I have plenty of identical (that is, the same title) tabs open when one of them hangs. Using the Activity Manager to kill this tab doesn't work since they all have the same name. Are there any extension or other method that allows me to kill a tab using the mouse pointer, get a certain tab's PID or some other solution to my scenario?
You don't need an extension for that. In the Chrome Task Manager double click on a task to bring it to the front (also you should be able to identify the hanging task there, since it'll probably gonna use a lot of resources.)