"Do you know that your umbrella is wet?"
Translation:Wiesz, że twój parasol jest mokry?
There are two translations of the word "know". "wiedzieć" (1st person singular: wiem) is used for general idea of knowledge, therefore it's "I know, that X" or "I know about X", such situations.
"znać" (1st person singular: znam) is used when your familiar with something or somebody. So it's generally "I know X". Like "Yes, I know him" or similar.
Isn't "Wiesz, że wasz parasol jest mokry?" a little contrived as a right answer? "Do you know that y'all's umbrella is wet?" I mean, it's grammatically correct, but doesn't really seem to be a real world sentence. You'd be talking to a single member of a group in the second person, while still considering the whole group to be in the second person.
O.K. In that context I could accept this as a right answer, I suppose. It's certainly not the first way one would choose to translate the English.
As to y'all, it is non-standard English, used often in the south, essentially filling the role of wy in Polish. (Some parts of the Northeast would use "youse guys" for the same thing.) I only used it here to differentiate singular and plural you.
Should it not be 'Wiecie, że wasz parasol jest mokry?' as the second correct answer? The speaker seems to be addressing either one person, but in a formal way, or several persons (which looks less likely, if there were several persons, maybe there also would be several umbrellas).
It's accepted, but it will be starred now. There is a starred version "Wiesz, że wasz..." - it shows that first 'you' can be different from second 'you'. It makes sense to imagine that you meet your friend who is with another person, so the umbrella belongs to two people (plural you) but you talk specifically to your friend (singular you).
The sentence is "Do you know that your umbrella is wet?" - we can easily imagine "Your umbrella is wet" as a separate sentence. In this sentence, "your umbrella" is the subject, so it takes Nominative. and "swój" refers to the subject of the sentence, so it would be like "umbrella's umbrella".
"wiesz is conjugates in the singular person" - correct.
"wasz to the formal or plural" - no, only plural. Unlike French or Russian, this is not a formal way of speaking to one person.
So this is talking to one person (Sue) about an umbrella belonging to more people (Sue and Adam). Perhaps Adam is on the phone so that's why you're only talking to Sue.
Almost, you also need to translate "your" in "your umbrella", otherwise it's just "Do you know that the umbrella is wet?".
So for "pan", that's either "pana parasol" ("pana", just like "jego" or "jej", doesn't undergo declension) or "pański parasol" ("pański" does).
On top of this, while "Czy pan wie..." is okay, I'd say that Formal You is the only situation in which it is not only correct, but actually even more natural to put the subject after the verb: "Czy wie pan, że [pana/pański] parasol jest mokry?".