Translation:Please read page 7.
In this case "Page 7" is a proper noun.
A quick google - A proper noun is defined as "a name used for an individual person, place, or organization, spelled with initial capital letters, e.g., Larry, Mexico, and Boston Red Sox."
I do understand why a name, a city, a brand, etc. are proper nouns, but a page? unless it's THE page no one should miss, wouldn't it just be "the page 7" instead..?
How would you say please read seven pages, rather than please read page seven?
I guess you'd say something like "nanamai no pe-ji wo yondekudasai" (you'd use a counter)
You're pretty much right Dan, but I think it's more natural to put the counter after を. That is, 「ページを７枚読んでください」
I don't think the Duo course goes into the intricacies of Japanese numbering (where there are specific counters for round objects, long-and-thin objects, flat-paper-like objects, etc.), but i recommend Tae Kim's free Japanese grammar guide (Google it) to fill in the gaps this course misses.
I think both readings are possible, but you need to figure out the right one by the context. My guess is that "Nページを" references "page N", whereas "Nページ" means "N pages". Here are a few examples I found on WWWJDIC:
Making references to number of pages:
私は更に５０ページ読んだ。 = I read fifty pages further.
私は６０ページ読んだが、一方彼は１０ページしか読んでいない。 = I have read sixty pages, while he has read only ten.
Making references to a specific page:
９４ページを読んで下さい。 = Please read page ninety-four.
日本地図の３ページを開けなさい。 = Open your atlas of Japan to page 3
Maybe one way to remember this is that with the を afterwards, the word ページ is treated as a noun, while without the を, ページ is almost like an artificial "counter word"? I don't know anything about this, though, so maybe what I said doesn't make any sense.