1) No, you do not need to leave your property when a realtor is showing it. You must allow the property to be shown, at least on reasonable notice at reasonable times (so no locking the door or interfering with the showing), but you are not required to leave the premises, unless the lease actually has some clause or term stating that you must. The owner or realtor is, of course, free to offer you something to leave--e.g. a $20.00 gift card each time, to take your family to Starbucks or Dunkin Donuts; but it would be up to you to accept or not.2) When there is a lockbox, the realtor must take reasonable care to secure your property. If he or she does not, he or she could be liable for any theft, damage, etc. resulting from the lack of care.