Let's use thou as singular you , and you as plural you and see
Twój tygrys- Thy tiger
Twoje tygrysy- thy tigers
Twoi bracia- Thy brothers
Wasz tygrys- Your tiger
Wasze tygrysy - Your tigers
Wasi bracia- Your brothers
I used brother/tiger because while both are masculine, brothers are masculine personal, and tigers are not-masculine-personal
I guess Duo assumes you already know ty/wy difference and now puts more importance to wasz/wasze/wasi distinction
yes, its tricky because doulingo does not distinguish between plural possessor and plural possessed.
wasz/wasza/wasze is one thing owned by 2+ people
wasze/wasi are 2+ things owned by 2+ people
twój/twoja/twoje is one thing owned by one person
twoje/twoi - are 2+ things owned by one person
note that wasze and twoje can be both plural (not masculine personal) and singular (neuter). This is a rule in nominative for all adjectives and personal pronouns (mój, twój, nasz, wasz).
Yes, it's still used and modern. It's not archaic or biblical at all, nothing like thou. In normal conversation, the "you (familiar)" conjugation of the verb makes the word ty redundant. However, it's very often said in emphasis or imperative or specifying "you" out of several people.
I'd add, that only nominative "ty" (and in the same relation Ja=I,my=we, wy=pural you) is less common, as Polish language uses those pronouns as subject less often than English does.
In all other cases, and the possessive pronouns like twój/wasz are used every day. Singular second person verb forms are used.
Every time you talk with one person that you are on first name basis - you use forms of "ty", "twój", and verb forms that match. And if you are talking to a person who you need to be polite to- you use Pan/Pani/Państwo, not "wy".