Translation:Inside the train, please do not talk on a cell phone.
話をする means "to have a conversation" / "to chat". 話す itself is just "to speak". Therefore, it's more natural to say 話をする when talking about having a conversation on a cell phone.
Sorry, I don't have better explanation than this, but using just 話す by itself sounds quite bare and unnatural to me in this sentence. I don't think there are any established grammatical rules concerning usage of 話をする / 話す, it depends on what you want to say.
As of 12.13 this question is still marking translation of "けいたい電話" as "cell phone" wrong. Obviously you're not on a landline, but if we're going to be literal and translate "電車の中で" as the odd "in the train" (rather than the more natural "on the train"), this is confusing.
This one definitely needs a bit of work. At the very least, "cell phone" and "mobile phone" should be accepted. In addition to -- or, arguably, in preference of, "phone" since we're specifically using "けいてい 電話" and not simply "電話" It looks like there is not much disagreement here and the Duo folks just need to fix it.
Well, technically "Please don't use your cellphones inside the train" would be "電車の中では、携帯電話を使わないで下さい" and it means something different from "do not talk on your phone".
In your translation, you would not be allowed to use your phone at all. That is not what this sentence means, since this only says you may not call someone (probably because it's considered rude) but you can still play games or surf the web provided it's silent or you have headphones.
Sometimes it feels like Duo is so focused on being literal with the translation (vocab AND grammar), that it just completely forgets to concern itself with whether the sentence sounds at all natural in either of the languages... And the fact that it only happens sometimes, ie. it's completely inconsistent with it - makes the issue a whole lot worse.