Law /
Uber in Poland - illegal [28]
That's about fines for drivers. If you check the Uber website (as a regular and happy user I recommend it to any expat or local) you will see details about their insurance.
Not that a passenger need be interested.
They really are good. If you were genuine, and not a taxi operator pretending not to be and trying (badly) to do a free advert, I'd recommend them to you too.
I would seriously avoid this taxi firm you're trying to push - too many posts from yourself pretending not to be adverts, whereas in fact one radio taxi is much the same as any other.
One reason I prefer uber.com/cities/gdansk
Also worth mentioning that (an alternative to taxis) the new fast rail link from Gdansk Airport to Gdansk centre (with good connections to Sopot and Gdynia) is now open.