one definition for thankfully - let us be thankful that; "thankfully he didn't come to the party" -- this way, it can be used :)
No, carteira is wallet. That flat thing where you keep money and credit cards.
A woman's Wallet is called a purse in British English. If not completely right technically, it is certainly in spoken language. Women's purses are normally slightly larger than men's, often containing hair accessories as well as money and credit cards, at least in my limited experience ;). Not sure if there is a different word in Portuguese for a woman's wallet?
no, there isn't a distinction. But if you go to a store to buy one, you can use "carteira masculina" or "carteira feminina".
I didn't try to see if would be accepted, but it sounds more natural to my ears to invert the sentence to "Fortunately, she found the wallet."
is the sense of felizmente different than the more literal "happily" or is that OK too
it didn't say that "found" was a meaning. it only showed "met" so......