As a project manager how you handle this situation?

While I am not a project manager, I don't think these issues have anything to do with project management. These issues are usually dealt by company policy which generally is being adopted by higher management and enforced by line managers and HR.

If you have a project that has to "deliver" some ideas about what should be done to improve productivity then you probably need some sort of subject matter experts in this area to come with some recommendations. I don't know if such experts do exist.

Nonetheless I can't see how such a project could delivery anything other than some recommendations since policy making is the responsibility of higher management.

Trying to enforce rules such as: the employees can't use their mobile phones for more than 30 minutes per day most likely will irritate them and probably the productivity would go down, but that's just my personal opinion. Also I don't believe that such studies are accurate.

From the project side, I would check corporate policies are there anything in the organisation assets on the subject?
If not I would try to influence the organisation in putting in place appropriate rules. I would see what rules can be put in place within the project.Aaron suggestion on that part look good to me.
On corporate equipment some restriction are possible, Deepesh summarized it well.

Assuming that this is a project, there are two approaches I would consider.

First, the easy approach, based on the description provided:
A) Establish a policy for personal phone use. It has to be enforceable, so there should be some flexibility in it.
B) Assuming that the school email and internet are managed centrally, use filtering tools that block content and prevent access to sites based on defined categories. Also look into endpoint security tools that can identify potentially unsafe sites in search results.

Second, the longer approach:
A) Go back to requirements. Work with your sponsor and stakeholders to define your current state and desired state.
B) Conduct a gap analysis and identify solutions that will help you achieve your desired state.
C) Determine which solutions to pursue and then plan/execute.

Regardless of your approach, make sure your sponsor clearly defines completion criteria, so that you know how to determine when you are done and successful.

There are technologies to implement website filters for denying access to 1) Pornographic 2) Gaming Sites. These are routinely implemented in corporate organizations and Educational institutions. You can also deny access to specific social media websites like Twitter and Facebook.

Anything can be controlled or locked down on Corporate or university computers.

The access rights to install software is routinely limited to the technical support staff at corporate offices or universities.

personal Mobile phones are not on corporate network therefore no policy or organization can restrict content being distributed through these mechanisms for the fear of discrimination against citizens who legitimately need to be contactable for family emergencies or are special carers.

Whilst kids under a certain age can have mobile phones which have restricted access, and its the responsibility of parent or guardian to ensure the restriction, You will find it extremely hard to enforce restriction on adults.

Off course if anyone is caught engaging in malpractices like exchanging pornography or harassment using technology, they can be officially reported to the authorities.

One thing that can be done is to enforce a policy to stop the employee from talking or using a personal mobile phone within a work premises if it's reasonably quick for them to leave the lab or a lecture room and attend to that personal call. You can also have a policy for them , not to spend any more than 15 minutes at any given time unless emergency and personal justifiable situations force them to.

Dear Deepesh,

According to a 2016 University of Nevada study, employees using working hours for non-work activities costs U.S. companies as much as $85 billion a year. As discovered by CareerBuilder.com, adverse consequences of wasting time at work include:
Loss of revenue
Compromised quality of work
Missed deadlines
Negative impact on boss/employee relationship
Lower staff morale
Negative impact on client relationships.

Do you think that use employees performance tracking may overcome above problems?