You use quarks as your one example of something that is not emergent. However, how can you prove that quarks are not a system of smaller interacting particles?

This misses the point. 'Quarks' were a stand-in for whatever particle you take to be fundamental; if there's something smaller than quarks, that does not defeat the notion that it is unhelpful to describe the action of the stock market in terms of its non-quarkness.

As for emergence, the way I understand Emergence based on this post and the comments is that emergence is a result of the parts of a system interacting with one another, possibly limited to those event that were not predicted.

In what way is this a useful concept? In particular, having not been predicted is a feature of the predictor, not so much of the event, and so attaching the adjective to the event invites thinking wrongly that 'emergence' is fundamental to the event.

insisting that a word is terrible just because it was used wrong by some people is obviously an ad hominem argument.

It is not an ad hominem argument. I know that because you club baby seals and you claimed it was an ad hominem argument; therefore, it is not an ad hominem argument. The previous sentence is an example of an ad-hominem argument. There are of course other varieties of ad hominem, but it isn't any of those either.

Just because some people use it wrongly does not mean it can't be used correctly, and replacing it with magical is simply non sequitor.

It is really not a non-sequitor. The point is that 'emergent' tells you about as much about the phenomenon as 'mysterious'. It doesn't communicate much more than "I don't understand why this happened" - as you grant above.