Can you use your Steam wallet on other websites [green man, etc]

Not as far as I know.

no

You can't.

Nope i would love to be able to do that :/

if it's STEAM wallet it's an only STEAM wallet...

you can buy tf2 keys with the money of your steam wallet from the community market and then use them to trade for games or sell them for paypal money which then you can use on gmg and other shops.

direct use of steamwallet outside of steam isnt possible.

no.. that is valve's money. is like store credit.
well... technically, you can buy a game on steam, and then sell it for paypal funds, but you know...

Nope, Valve really wants your money and so wouldn't let you waste your money anywhere else than Steam.