iPhone/iMessage question
iMessage is connected with your iCloud E-Mail-Address as well. So if somebody unlocks your iPhone, this person will see all of your messages.

This Apple Support document describes the ways necessary to stop iMessage on your lost phone:


  If you didn't turn off or deactivate iMessage before switching to a
  non-Apple phone, other iOS devices will still try to use iMessage to
  send text messages to your phone number.
  
  If you still have your iPhone, follow these steps to turn off iMessage
  and deregister your phone number:
  
  
  If you transferred your SIM card from the iPhone to a non-Apple
  phone, put it back in the iPhone.
  Make sure that you're connected to the cellular data network. 
  Tap Settings > Messages and turn iMessage off.
  
  
  If you don't have access to your iPhone, or if you can't deactivate
  iMessage from your iPhone, please contact Apple Support. Support for
  this issue is free.