"I need the names of the nineteen girls."
Translation:Potřebuju jména těch devatenácti děvčat.
You are here to learn Czech, remember? Or are you here to convince us that you know better Czech than us?
"Potřebuju jména devatenácti holek" means "I need the names of nineteen girls" - it means any random nineteen girls, in both languages.
There are many situations when the English definite article doesn't correspond to anything in Czech, such as, for example, in "the names" in this exercise (it's optional to say "ta jména"). On the other hand, in other situations, Czech observes the difference by using demonstrative pronouns. There are borderline cases where the demonstrative is optional, and there are cases where it must be present, or where it must be omitted.
If you start observing the examples throughout this course, you might eventually grasp the pattern and stop making mistakes yourself. Don't blame your mistakes on the course contributors, who are, I can assure you, quite proficient in both languages.
It definitely primarily means "from", more accurately "from within, from the inside of" (as opposed to "from the vicinity of" or "from the time of", which is "od") - e.g. "Jsem z Prahy" (I am from Prague) or "Beru košili ze skříně" (I'm taking a shirt from/out of the wardrobe).
The English "of" is primarily the Czech genitive case without any preposition.
But there are situations where English uses "of" and Czech needs "z + genitive". Specifically counts like "one of five" -> "jeden z pěti", or materials such as "It's made of wood" -> "Je ze dřeva" (but English can also use "from" here).
Cool. Again, as a beginner (well, one year almost now), our first glimpse of Z was in context of "jeden/jedna/jedno z tech... etc." so hence the confusion for those of us "early on" in our studies. Actually, I just caught this YESTERDAY from another discussion. So it's new to me.