Is it Web site, Website, web site, or website?
It’s Web site and Web page.
Because Web is short for World Wide Web, it should be capitalized as a proper noun.
Most style books, including The Chicago Manual of Style, and most dictionaries, including Merriam-Webster, mandate the two-word spelling with Web capitalized. The same goes for Web page.
The Oxford English Dictionary, on the other hand, prefers a more progressive spelling: website.
Email, e-mail, or E-mail?
Either e-mail or email, depending on whom you ask.
Although Google and Yahoo use email, the New York Times and other authoritative publications prefer e-mail.
It’s true that American usage tends to drop hyphens over time (so decision-maker is now decisionmaker). But when a single-letter abbreviation functions as a syllable on its own, the hyphen remains: X-ray, T-shirt, A-frame—and e-mail.
Internet or internet?
Not much disagreement here. Internet is a proper noun and is thus capitalized. Even as an adjective—Internet source—Internet takes a capital I.
You can use internet, however, for any other network that exists between two locations.
Online, on-line, or on line?
It’s online or on line, depending on what you are doing.
When you log in to a Web site, for example, you must provide your login credentials. But you never login. Rather, login is an adjective, while log in is a verb.
Similarly, online is an adjective, while on line is a prepositional phrase. So, for example, you do online research to find cases on line.
Unlike e in e-mail, on is not a single-letter abbreviation, so the hyphen is not necessary.