How do I search to see if phone is being shard with another device

A phone cannot be shared with another device. However, multiple devices can share an iCloud login. You should only do this for devices that are used by one person; 2 different people should never share an Apple ID/iCloud ID. You can see all of the devices that share an Apple ID by going to Settings/[your name] and a list of devices will appear at the bottom of the page. You can also log in to https://appleid.apple.com to see all devices that can share an Apple ID or https://icloud.com and click on Account Settings.

No one can monitor your phone unless it has been hacked (which requires physical possession of the phone to actually hack it), however, someone you share an Apple ID with can share anything that you sync to iCloud.