Do you always have to spell Internet with a capital?

Answer 1

It may or may not be capitalized. You should refer to the style guide for the venue being used.

The word "internet" is subject to debated style usage. Although the global system may still be referred to as the "Internet", it is rare for the generic term "internet" ever to be capitalized in non-academic use. The number of publications that still use the capitalized form is rapidly dwindling.

Although some sources (notably on Wikipedia) continue to use the capitalized form, even these recognize that some style guides that do capitalize the noun do not capitalize the adjective form, e.g. on the Internet, internet connection.