To answer your first question: yes, you can limit or even prohibit the use of cell phones during work hours. Employees can be expected to give their undivided attention to the work you pay them to perform, and if that means cell phones need to be turned off or put away, you are entitled to make this request. However, employees should be allowed to use cell phones during their break and meal periods, as this time needs to be truly their own in order to satisfy the requirements of state law. Fair warning: if you attempt to prohibit cell phone use during all non-break time, you may receive some fairly aggressive pushback. A more lenient policy may do the trick. Our standard language says, "Personal cell phone use should be kept to a reasonable limit during working hours. Reasonableness will be determined by your manager." This language gives your managers considerable discretion, but they should be trained to use the same standard of reasonableness for all employees to avoid claims of discrimination.
To answer your second question: no, audio, video, and photography cannot be strictly prohibited, but they can be limited. The National Labor Relations Board, which enforces the National Labor Relations Act, has said that employers cannot outright prohibit recordings as this could interfere with employees' ability to organize with respect to their terms and conditions of employment. For instance, employees might choose to record a conversation during their lunch hour related to asking for raises, and want to share that recording with employees who work different shifts. This would need to be allowed. However, you can still have a policy that prevents recording (via audio, video, or photograph) confidential information, such as proprietary business practices, customer lists, client or patient information, or employees' personal information. Be aware that you cannot deem all information confidential, e.g. "all conversations in the office" or "anything related to customer/patient care."
If you feel it is important to have such a policy (for reference, this is not one we generally include with the handbooks we make for clients), I suggest something like, "Audio and video recording devices, including cameras and smartphones, may not be used to record or capture any confidential information, whether it is proprietary business information or clients' or employees' confidential personal information. If recording non-confidential information, e.g. taking photos of colleagues, please seek the consent of all parties to the recording." A policy like this can be added to your handbook during your next handbook review, or if you feel the need is urgent, you can distribute it to all employees now and have them sign an acknowledgment form.
-Columbia EDP HR Resource Center