I hit the Compose key and then =/ gives ≠, but I don't seem to be able to enter ≈. For that and more obscure characters I'd open Emacs and run insert-char.
It's just compose ~ ~ (tilde tilde). The compose key sequences are often the most logical thing you can think of. Emacs C-x 8 is good but you have to try and guess the unicode name of the character.
It's the interrobang. It literally means "?!" Like WTF?! But in one symbol. It mattered when "cost per letter" or typesetting spacing mattered. I still like it and use it often enough. As for chess, honestly, yeah, it could be used for that.