Will we encounter any passport checks on the NL -> PL leg?
No; passport checks within Schengen are only allowed to happen to verify your ID and nothing else. At the moment due to the pandemic they glance at the passport and your NHS Vaccine Pass (purely to be sure the NHS Pass is yours) on the way to the baggage hall at Okęcie. They don't scan it (they were just standing in a corridor looking relaxed) and it all took 5 seconds max.
Will my wife be challenged for presenting a British passport to the Wizzair check-in agent?
I came back here about a week ago. I came via Vienna rather than the (slightly) cheaper Amsterdam because Amsterdam wanted a PCR covid test but Vienna is fine with just the NHS Vaccine Pass. I went Manchester-Vienna Warsaw, was there by about 8.30 pm and it wasn't dear booking direct on Austrian Airlines' website.