Translation:It's a quarter to five now.
According to Google Ngram Viewer, "It's quarter past" has overtaken "It's a quarter past" in frequency of usage in British English in the last 15 years or so, and is also becoming more common in American English. "It's quarter to" still trails "It's a quarter to" in usage frequency, but not by a very wide margin. So "It's quarter to five now" definitely should be accepted.
https://bit.ly/2FbApB8 (click on "Search lots of books" to generate the graph)
My knowledge of the Chinese language isn't good enough to comment on whether or not the "now" is necessary in this sentence.
No, "now" is Chinese-speak; is just a literal translation, which makes the English sentence look like someone translated it from another language. It's as if you were to read a dialogue between two friends meeting , one of them says : "你 吃 了 吗？“ and translate that as :"Did you eat?" when actually, you want to translate it as (for instance): "How is it going?" .....
In college, I was taught that this sentence should be structured "现在五点差一刻“ This is also the structure that the Pimsleur audio courses use. Does anyone know if it matters if"差一刻” comes before or after the “五点”? To me, the given sentence seems grammatically incorrect, but I'm not a native speaker.
The radical meaning of 差 is "difference". When something is "bad", its difference from the standard is being noticed, and thus 差 is extended to "bad". It would need some comparative words to mean "worse".
我今年成绩很差/My results are bad this year.
拿个B 也没差/There's no difference getting a B.
我一直拿A 的！差很多了！/I used to get A! It's much worse now!
I for one think the now is absolutely necessary (现在). You don't want to just translate every sentence into "perfect" English because then you will just be relying on rote memory rather than actually understanding the characters and the Chinese sentence structure. I actually wished duolingo allowed more "dirty" English rather than sometimes requiring one commonplace Chinese phrase to be translated into the similar commonplane English phrase. Just because they're often said in the same context in each culture doesn't mean they hold the same meaning!
This is very sensible and inspiring for language learning, and deserves a lingot. In English we use the impersonal It to tell the time but such structure is much less used in Chinese. If someone says this without "now", it would become a bit difficult to tell what he's talking about, unless we already knew Time is the topic.