We weren't too sure about this one in instances were multiple cards are discarded

"After a card is discarded from a players hand..."

If I lose an intrigue challenge and pay a claim of 2 cards ... can I trigger Brightwater and if so, can I choose which card to return

Each card discarded from hand creates a separate and distinct "after a card is discarded from a player's hand" Response opportunity. So yes, you can choose which card you are Responding to when triggering this Response.

I take it this is true for many similar affects ...

Whether discards for intrigue or any of multiple Greyjoy discard from deck effects, often resulting in multiple cards being discarded. When I want to trigger a response, such as Fishmongers Square, I can wait until all cards have been discarded and then make my choice

So same with Brightwater, i.e. I do not have to make a decision after the first card is discarded and then find I have blown my opportunity

You have to fully resolve an effect before triggering a response to it (other than a save or cancel). Also, I believe the only cards discarded sequentially (by a single effect) rather than simultaneously are those discarded from a deck (and I'm not even sure about that).

"Sequentially" vs. "simultaneously" isn't really the point. No matter which, each card discarded creates a separate, individual response opportunity, so you can always choose which one you are responding to. And as Khudzlin says, it's not like you can break into the middle of an effect that discards more than one card from anywhere with a response. Except for "saves" and "cancels," you can't interrupt effects in this game.

Are cards discarded from the top of a deck discarded in the order they come?

Yes. If multiple cards are discarded from an ordered set (which pretty much just means your deck at this point), they go to the discard pile in that order - unless you are specifically told otherwise, of course.

Thanks.

Side note, this location allows you to put Darkstar back into a players hand after he has been "discarded".