Yes, the name of the LLC can contain your initials. I believe what you heard was that an owner's personal finances should not be linked to the LLC's finances or you can risk being held personally liable for things that your LLC were meant to protect you for. For example, if the LLC makes...
Yes, the phone would be considered "personal effects" in this situation. However, the policy doesn't say anything about a seizure, i.e. they wouldn't be able to take the phone away from the student under this particular clause.