Passport check for non-EU(Wizzair)

I'm an Israeli flying from Gdansk to Turku with Wizzair, checking in online with carry-on bag only. My plan was to go straight through security to the gate. However, I noticed on their website that non-EU citizens are required to have their passport and visa checked, and their boarding pass stamped, or else it would be invalid and boarding could be denied. I haven't actually printed my boarding pass yet because online check-in is still closed.

So here are my questions:

• What happens if I use a mobile boarding pass? How do you stamp those? Is Mobile boarding pass even available in Gdansk airport?

• How strictly is it enforced?

• My flight is early in the morning, so I would appreciate saving time and not have to be present in the airport earlier than necessary. Waiting in line for the check in desk can be troublesome. However, I land in the same airport a few days earlier so I figured, would it be possible to have it checked and stamped in advance? Alternatively, can in be done in the city terminal a day before the flight? What can you tell me about the terminal in Gdansk city centre? What services to they provide. I know Wizz has representatives there but do they offer check in services? Or better yet, Wizz also have desks in Tel Aviv Ben Gurion airport. I actually fly to Gdansk with Lot and not Wizz, but perhaps I could take care of it as soon as possible?

On a different subject:

• Middle name: My brother has one(we're flying together), it's on the passport but I didn't know when booking so it's not on the ticket. i.e John Smith on the ticket, John Patrick Smith on the passport. I know it's been asked many times, just from a quick search I found dozens of answers. Everybody said they had never had a problem. But when I wrote Wizz and Lot, they both said I should change the name, and of course they want a fee that is higher than the price I paid for the tickets. I'm not willing to pay that as a matter of principle but I don't want any trouble. Did they give me that answer just so I pay the fee or is it really a big deal?

Thank you kindly for your time.