Can an iphone be tracked if it's turned off? Or being restored?

If an iphone 5s or any other iphone model is lost, could it be tracked using find my iphone if its turned off or not connected to the internet? Could it be restored? And if it can would that stop it from being tracked using find my iphone? I lost my iphone

No, if it is off then of course it can't be tracked. Depending on what connection it may have access to in the past, your security settings and/or if you have an active data connection on at the time then it could connect to the internet.

Again, depending on the connection, security etc it could be restored, but iCloud Activation lock would require the Apple ID & password to do anything beyond that.