Thank you for your interest in Telerik Test Studio.
Unfortunately I have to admit that Exploratory testing is not supported for Firefox. However this feature could be used in both IE and Chrome.
In the future it is planned to integrate Exploratory testing in the Test Studio itself. Though there is no estimation when this will be implemented.
From your screenshot I see that the other two extensions in Firefox are also disabled. To fix this please first upgrade to the latest Mozilla Firefox available. Then you could use the following article
how you could calibrate the browser manually in case the automated calibration is not successful.
Please do not hesitate to provide details in case you need further details.