"Mówisz po polsku."
Translation:You speak Polish.
The nominative form is "polski". It's true that most of the languages end with -ski: polski, angielski (English), duński (Danish), francuski (French), or chiński (Chinese). But there are also some exceptions: niemiecki (German), niderlandzki(*) (Dutch), szwedzki (Swedish), grecki (Greek).
(*) "holenderski" is also correct
po+ adjective +u - in a specific way
WSJP.pl dictionary does not have definition for "po", but has various definitions for "po+ adjective+u"
1) in a way that is considered typical to Africa, it's sights, climate, geographical circumstances, and way of functioning/
2) in a way that is seen as characteristic to inhabitants of Africa/ 3) in a way that is seen as according to traditional culinary receipts of inhabitants of Africa
po królewsku= in a way that is seen as typical for a King and Queen/according to a refined recipe for a dish
po bożemu= in a way that agrees with moral rules of one religion/ (joking) in a way it is supposed to be
po inżyniersku-in a way that is perceived as characteristic for an engineer
po polsku= 1) in a way that is characteristic to Poland it's geography, sights, way it functions, culture, history, economy 2) in a way that is perceived as characteristic to habitants of Poland 3) in a way that is assumed to be according to traditional recipe of inhabitants of Poland
4) in Polish language
po ojcowsku - in a way that is seen as characteristic for a father
po Warszawsku - in a way that is perceived as characteristic to inhabitants of Warsaw/ in a way that is assumed to be according to traditional recipe of inhabitants of Warsaw
I think we can agree that all those have something in common (in a way that is perceived as characteristic to someone/somewhere)
And there is no way "po ukraińskiemu" is in any way correct in stadard Polish. I don't know if it's just a common mistake or it exists in some regional forms or as calque from other Slavic language.
You can do that, especially if you want to be unambiguous, but it's not required. To create a yes/no question all you need is a change of intonation (when speaking) or a question mark (in writing). Note that this TTS intonation is… unreliable, so you should try finding other sources to learn that.
Indeed it's not, although you may occasionally see a person incorrectly capitalizing it, especially if influenced by English (and the other way around, Polish people who forget to capitalize it when writing English).
In Polish, all adjectives are normally lowercase, even if derived from the proper noun (and language names are essentially adjectives). On the other hand, the names of nationalities (people) are still written uppercase, while the names of particular city dwellers are lowercase. Even I find it crazy and I bet the change was at least discussed among the regulating body in recent years.
I meant, it makes no difference how many people you are actually talking to, only how many people you are referring to. I should have phrased that differently.
Imagine someone is a member of a politcal party which is against the implementation of a miminum wage law. Then you might say to that person: "Wy mówicie (cała partia), że takie ustawy negatywnie wpływają na wzrost gospodarczy, czy nie tak?"
That is why your "rule" seemed confusing to me.