"These people eat ducks."
Translation:Ci ludzie jedzą kaczki.
I don't understand why it is "Ci ludzie" and not "Te ludzie". I thought that "ci" only could be used for a group of male persons, and that "te" could be used for all other plurals. I am obviously wrong, so could anybody explain what the rule is?
You are close. But it's not "a group of male persons", it's "a group with at least one male person". Even if it's 999 women and one man, it's still grammatically masculine personal. Other than that, you are right. And as "people" have at least one man (otherwise you'd say "women", after all), it's masculine personal.
What is the difference between "Tych" and "ci"? When should I use one or the other?
Ci - Nominative
used with subject.
Tych - Genitive and Locative
Gen - used with negations, describes object: Nie znam tych ludzi - I don't know these people.
Loc - used with about - o, describes object: Mówię o tych ludziach - I am talking about these people.
"jeść" takes Accusative for the thing eaten.
Your sentence (using Instrumental) is actually grammatical. But it means that they use ducks instead of forks and knives. A rather strange thought ;)