Barry,
notes sound twice, but first from the keyboard itself, and then from the PC speakers (softsynth). (You can achieve the same thing as Local OFF by just turning the vol of the Casio all the way down, right?).
The closest description I can give, is that it sounds like a very fast echo, but from different sources.

I have heard midi echo from the casio before, using a PC sequencer, and the notes were so close together that they sounded like a phaser effect, or some times cancelling each other.

I can understand that there HAS to be a lag, but it seems it is longer than the 10 ms. It seems that the "reported" latency is 10 ms and the "actual" is more like 50 ms or longer, but DEFINITELY smaller than the internal PC synth lag.

It doesn't bother too much, but there IS a difference in the way the keyboard reacts. Certainly, it can't be recognised by a listener, but If someone with a little experience plays the instrument they will surely detect a "sluggishness" in the way it reacts, due to the latency. Sometimes feels like walking in the sand very close to the sea. You are walking fine, but something is wrong.

Anyway, your remarks about possible midi problems, have to be checked thouroughly before I say there is nothing wrong with them, but for now it just doesn't seem like a midi problem to me.

I have friends that own a "mom and pop" computer store, and I have earranged to borrow a SB live they have around, to see if things better. If yes, with about 70 €, É can buy an Audigy 2 ES or something from them which reports "Very low latency" in the specs.
Anyone with experience in that line of cards??