it is a Question word.
Any(...)
combining で + も, getting you a sort of "no matter which one it is". Combining Question word with でも like 「誰でも・いつでも」 makes it like any+question word
誰でも Anybody
いつでも Anytime
どこでも Anywhere
or something
whennoun＋ , implying it is a suggestion. Basically same use case as nounか何か
お茶でもしない？ You wanna do tea or something?
ちょっと時間があるからゲームでもしましょうか？ Since we've got some time, wanna play a game or something?
電車を待っている間にこの雑誌でも読んでください。 iWhile waiting for the train, please read this magazine or something.
even (you can do it)
この漢字は日本人でも間違える Even japanese people get this kanji wrong.
大丈夫だよ、お前でも出来るよ。 It's okay, even you can do it!