The particle demo can follow an interrogative word to form a free-choice expression such as 'anyone,' 'anything,' and 'anywhere.'
Essential Japanese Grammar by Masahiro Tanimori and Eriko Sato, page 167.
Some provided examples with 何でも:
I can eat almost any (kind of) food.
Any drink is fine.
When followed by mo, the meaning of the phrase is GENERALIZED, meaning something like 'every, all' if the predicate is affirmative. However, it means 'no, none, not at all, not any' if the predicate is negative. Phrases consisting of INTERROGATIVE + mo occur more often with the negative than with the affirmative. In the affirmative, phrases of the type INTERROGATIVE + de (COPULA GERUND) + mo are often used instead.
Basic Japanese by Samuel E. Martin and Eriko Sato, chapter 8.1
Provided example with 何でも:
I ate anything.
Although the above translation is grammatical, 'everything' could also have been used.
In another book, I came across the following sentence:
That child is so bright he learns everything quickly.
Essential Japanese Vocabulary by Akira Miura, 頭 head.
In this case, 'everything' is used instead of 'anything.' Both are possible, though.