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1. I enjoy browsing the Internet.

2. I don't plan to go into the office tomorrow. I will work from home.

In sentences above, is the article 'the' needed? If yes, is the need for the definite article similar to the common phrase 'in the hospital'?

3. email or e-mail

4. cell phone or cellphone

Thanks in advance
Comments  
email, e-mail and E-Mail all are right.

btw: why is Internet always with a capital letter?
personally, i feel that "internet" and "website" are more idiomatic, but the grammar gods still prefer "Internet" and "Web site." Here's a quote from the Chicago Manual of Style Q&A :

Q. Which is currently accepted: Web site, web site, website, or Website?

A. A lot of people are writing “website.” A lot of people have come to prefer “website.” But formal usage still calls for “Web site,” in recognition of the initiatives of the World Wide Web Consortium (write “Web-site” as an adjective). The most elaborately formal modern American publication I can think of, the New Yorker, still writes “Web site,” but then again, they also write “E-mail,” “coördinate,” and “reëxamine”—they are very particular. We at Chicago are very particular too, and we recommend “Web site.” But our press as a whole is not in the position of publishing a single, unified publication—such as a magazine. It is easier to apply a set of standard rules and never vary from them for one publication, but rules applying to all sorts of books, articles, and other writing must be a little more flexible. Moreover, when a word gets used a lot it tends to lose any awkward edges (and what could be more awkward than a compound formed of one capitalized word and one lowercased word?). Each new book that appears on the scene presents an opportunity for an author to express a usage preference or to demonstrate a familiarity with changing usage.

But generally, I would recommend “Web site” for formal writing, but “website” for informal writing or friendly writing. Unless, of course, you prefer “Web site” even when you’re being friendly.
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Thank you. It's interesting that there are "conversations" about things like that.

I prefer this one:
But generally, I would recommend “Web site” for formal writing, but “website” for informal writing or friendly writing. Unless, of course, you prefer “Web site” even when you’re being friendly.
Spinnaker, the Chicago Manual of Style has a great monthly Q&A, and the editors who write it can be very funny. While it's helpful to actually have a copy of CMOS, you can access their Q&A without it. Many people think that CMOS is "clunky" (and I would agree) but it's full of good stuff.

www.chicagomanualofstyle.org/CMS_FAQ/new/new_questions01.html
Thank you for the link, GGEmotion: smile
Students: We have free audio pronunciation exercises.
Grammar GeekSpinnaker, the Chicago Manual of Style has a great monthly Q&A, and the editors who write it can be very funny. While it's helpful to actually have a copy of CMOS, you can access their Q&A without it. Many people think that CMOS is "clunky" (and I would agree) but it's full of good stuff.

www.chicagomanualofstyle.org/CMS_FAQ/new/new_questions01.html
Yes, thank you for the link. It's interesting to read this Q&A, but I will never post there any question, because of my worse English.