Door won't lock when it is open. Is this normal?
 

On my previous E class, when my door is open, I can press LOCK on my keyfob. And when I close the door, it will be locked.

On W222, if I press LOCK when my door is open, I can still open the door when after I close the door, although the alarm will sound.

Is this normal?

This appears to be normal with the driver door.
If the driver door is open, and I press lock on the key fob, all doors lock except for the driver door. When I shut the door, the lock still remains up. I have the Keyless Go, so when I grab the handle it unlocks all doors anyways so I didn’t test the alarm going off. I’d imagine if someone else without the key fob came and opened the door, it will open an alarm will sound (since the door remains unlocked). What I find odd is, the front passenger door doesn’t behave this way. If the passenger door is open and I lock the door, all doors lock, including the open door. I can shut the door and it remains locked. Weird design?

Yes, this is normal for the W222. The system is designed to prevent accidental lockouts by allowing the door to remain accessible until manually locked after closing, though the alarm may trigger.