Search:

Go for it. Nothing stopping you.

You don't even need to use the wallet. You can store some at BTC-e. Just have an account there. Under the Finances section click "Make a Deposit" under the LTC section. This will give you an...

Get a Litecoin address too. You can swap Bitcoins/Litecoins here.
https://btc-e.com/exchange/ltc_btc

I dunno what exchange you're using, but make sure to do the verification process on whatever...