Is browsing Islamic websites during free time at work considered unlawful (haram), and what is the ruling on sending further inquiries?

If an employee finishes their work, there is no harm in them engaging in activities that are not forbidden. It is permissible to use work tools that are not affected by use, such as using free internet. However, it is better to seek permission from the employer. As for what is affected by use, or if it constitutes a distraction from the intended work, it is not permissible except with permission, because the time belongs to the employer. It is advisable to seek permission from the employer for browsing the internet or anything else that benefits one in the afterlife.