Dziecko sounds like "jyets-ko". Is that correct, or should it sound more like "jyech-ko" (with the English ch sound, as in "charge")?
TTS says it a bit wrong, but English ch would be even worse.
Polish "c" is described as "ts" in English so there is no better way of describing it, but it should be one sound.
Polish "cz" is English "ch", and Polish "ć/ci" is something like ch (cheat)
When I answered the translation exactly, it said that I was supposed to use "I've a child" instead of I have a child
I don't know why. If your answer was correct (and starred), it shouldn't say anything.
As for "I've a child" itself, Duolingo automatically accepts "I've" because it can be abbreviated like that in "I've got". That surely is an error, but we can't do anything about it.