The best way to handle this is not to modify the entered password, or to reject it, but rather to just display the message. If it stands out enough you should notice it and make the corrective action yourself. In your case no corrective action would be necessary.
It does "halve" the keyspace, by removing one bit of entropy from your password. This is assuming you only use letters in your password and not numbers or other symbols not affected by capslock.
Well, it's a bit tricky. Two inverted passwords still have different hashs. From that perspective, two inverted passwords are not equivalent and therefore the entropy is not decreased.
This is important because if you want to decode a hashed password using a rainbow table for example, you still have to hash the entire keyspace, not just half of it.
If you're doing an online attack, you can submit half as many passwords. I guess it's just as hard for an offline attack where you're cracking the database of hashes.
