Probably I'm not the right person to explain this as I'm not a teacher and I feel like all my grammar knowledge just disappeared since I was going to school... ;) Anyway, plural nouns can be masculine or feminine and masculine plural nouns can be personal (chłopcy) or non-personal. (psy). When it comes to non-personal nouns the adjectives bahave like the feminine ones. That's why it is "nowi chłopcy" (masculine personal) but "nowe psy" (masculine impersonal) and "nowe dziewczynki". (feminine) Check out this article. Scroll down to "Adjectives", there's a nice table showing the declension of "dumny". Wikipedia
By "personal" do you mean literally "describing a human person"? I've always thought that plural adjectives were categorized as either masculine animate and masculine inanimate/feminine/plural, and using those two categories, "pies/psy" would definitely be in the former, but apparently it's in the later. That'd make sense if it was personal rather than animate.
Personal nouns refer to people, non-personal (or impersonal) refer to anything else.
All personal nouns also count as animate.
The difference is only in the masculine gender in plural, since personal masculine nouns get their own set of endings for adjectives, verbs, numerals and themselves. All the other nouns: non-personal masculine, all feminine, and all neuter; get lumped into one pile called "non-masculine-personal" or something like that.
So in this sentence we have "chłopcy", a masculine personal noun in nominative plural, and "psy", a masculine animate but nonpersonal noun in accusative plural (which, for non-masculine-personal, is equal to nominative). That's why the adjective "nowy" gets the -i/y ending with shifted consonant, and the adjective "stary" gets the -e ending.
I think you should find some declension tables for adjectives online.
So you really only use the masculine plural adjective forms when describing male humans (or groups with at least one male human)?
That's kind of crazy weird. Are there any other languages that do this? I imagine other West Slavic languages do, but what about other Slavic languages in general, like Russian or Ukrainian?
AFAIK out of all major Slavic languages, only Polish distinguishes personal animate and impersonal animate.
East Slavic languages do not distinguish genders in plural, they only distinguish animacy, regardless of the singular gender of the noun.
Czech, Slovak, Serbian and Croatian distinguish between 3 genders in the plural, with some weird rules for mixed-gender expressions. Czech and Slovak also preserve animacy, but in plural masculine only. South Slavic languages do not preserve animacy in plural.
So it goes like this (parentheses contain N/G/A):
Masculine personal (robotnik/dělník/работник):
Polish: A=G (robotnicy/robotników/robotników)
Czech: 3 different forms (dělníci/dělníků/dělníky)
Russian: A=G (работники/работников/работников)
Masculine animate impersonal (pies/pes/пёс):
Polish: A=N (psy/psów/psy)
Czech: 3 different forms (psi/psů/psy)
Russian: A=G (псы/псов/псов)
Feminine or neuter animate (kobieta/žena/женщина):
Polish: A=N (kobiety/kobiet/kobiety)
Czech: A=N (ženy/žen/ženy)
Russian: A=G (женщины/женщин/женщин)
Any inanimate (stół/stůl/стол):
Polish: A=N (stoły/stołów/stoły)
Czech: A=N (stoly/stolů/stoly)
Russian: A=N (столы/столов/столы)
Oldboy doesn't translate nicely into Polish. You can say something like 'sportowiec-weteran' or use English word oldboy in Polish way: Oldboys competition - Zawody oldboyów. I am not sure if this is 100% correct way of writing. Borrowed words have their own rules. This is definitely not a topic for Duolingo.