One more thing regarding counting. Many Poles would do it: „Raz, dwa, trzy, ...”.
„raz” generally means „one time” but we can use it here.
Can you give any background as to why counting is done this way (as opposed to saying "Jeden, dwa, trzy...")?
Well, if you just say numbers one after another, they obviously take their most basic forms. So here: jeden, dwa, trzy. I wouldn't even think of gender here.
But yeah, some numbers can have genders, when they are paired with a specific noun phrase. Technically, the numbers ending with -1 and -2 can have genders. And thus "jeden" can be treated as masculine. jeden mężczyzna (masculine), jedna kobieta (feminine), jedno dziecko (neuter)... even "jedne drzwi" (not masculine-personal plural!)
For "dwa", it's obviously quite different. And quite complicated. "dwa" is the basic option, and it's used for plurals of nouns that are neuter (dwa drzewa, dwa pudełka) and "masculine, but not personal" (dwa stoły, dwa psy). Normally you think about "not masculine-personal plural", but not here, as there is a separate feminine option: dwie (dwie kobiety, dwie sofy).
And then you have "dwaj" for masculine personal (dwaj mężczyźni, dwaj chłopcy) and "dwoje", a collective numeral, needed for "dzieci"...
Welcome to Polish numerals ;) Luckily with other numbers it can be only the case of normal numeral vs the collective one.
Oh yeah, and the numbers also undergo declension. But that's enough for now, I think.