So, there is currently no penalty for offhand attack (say foe execution shot while wielding pistol and sword), no penalty for shooting a ranged weapon into combat, no penalty for shooting a ranged weapon while engaged.

Am I supposed to add a black die for these kind of things - sure I know I'm the GM so I pick when to add black die but I am wondering how the game was intended to be balanced.

There may not be an off-hand penalty per se, but I would consider not allowing any expertise dice to be added with an off-hand attack. Clearly it's a situation where it is hard to do your best.

It's my understanding that the dice should be added whenever you the GM feels it's warranted. I would at a minimum add a dice for an off-handed attack. Of course you may also decide that using an off-hand is actually a greater challenge and therefor add a <P>.

It's usually included in the action card. For example, in order for an Execution Shot to both shoot and melee attack, the pistol shot gains a <P> in difficulty. Just shooting a pistol (ie Range Attack) in the off-hand normally has no penalties, though. Like previous editions of WFRP, most people are assumed to be fairly ambidextrous or have minimal penalties for using an "off-hand", and the penalites mainly come when trying to do something with each hand in the same round. That said, I don't think it would be unreasonable for a GM to houserule adding a for any attacks/actions made with an off-hand.

I just picked up the set, but haven't read more than a few pages so far.

What are the advantages to wielding dual weapons?

In v2 it provided substantial gains, and so people wanted to take advantage of it all the time.

There are a number of actions available to characters that dual wield weapons...provided they spend the points to buy/learn them.

I've read through the rules twice and I'm not sure its clear what the differences in situation are to warrent a <P> vs. a ( I hope I got the notation right, the board could really use some dice icons )

I think after I've used them for a while I'll have a better feel but it's not clear yet to me what the difference is other than odds. I know you always start with a number of <P> dice based on you initial assessment and then fuzz that up or down based on smaller features. Is it more than that or clearer somewhere, or am I overthinking the issue?

The way I approach it is <P> is for base difficulty, or the inherent difficulty of the task. is for modifiers to the task.

In v2 terms, <P> would be the base difficulty of the task and would be any +/- you would apply.