score:7
Lock type (3) sounds like a 'deadlocking nightlatch'. Common in Britain, where I live, the one described here costs 20 GB pounds.
From the maker's website
Advantages: You can lock or disable the handle from working inside, this is useful if nobody is in the property. If someone smashes the glass (if it has glass) they canβt unlock the door. It also prevents the latch from being slipped. Disadvantages: If someone is in the property you could lock them inside. Lock Standard for Deadlocking Night Latch: Deadlocking night latches are not approved to British Standard (BS).
Security Note: A deadlocking night latch (non BS 3621) should always be used with a BS 3621 5 lever mortice deadlock for security.
How the lock is operated: Again a deadlocking night latch acts the same as a basic latch but with the extra feature of locking the latch with a key.
Upvote:5
That's also how most locks work in Spain, at least for points 1 and 2.
The first mode ensures that the default state is a locked door; you can't foget to lock it after you, as soon as you pull it closed it will engage (incidentally, many locks are trivial to open in this state without a key so not very safe anyway).
The second case is easily solvable as most people I know leave a key inserted at all times. The last one to leave the place takes the key from the door and closes behind them.
The third state is a bit strange, I've never seen a lock that doesn't fully engage from both sides; but I bet you can unlock it from the inside even in that state.