"Her decision helped a lot of people."
Translation:Jej decyzja pomogła wielu ludziom.
how come "ludzi" suddenly declines here, when in the other sentences it's just "ludzi"
Pomagać: komu? czemu? -- celownik (Dative). "Ludzi" is for Genitive and Accusative, which I guess you just encounter more often than other cases.
Also I may be wrong, but your comment sounds as if you treat 'ludzi' as the basic (Nominative) form, it is not, Nominative is "ludzie".
See wiktionary for declension.