My understanding is yes, you'd lose everything if your account is compromised, and yes if the site when down you'd lose access to the wallet for that time.

As far as I can tell, I don't think they give you a "wallet" exactly, instead they give you access to your funds in their system.  Effectively they act as your bank, but without interest (unless you count market fluctuation).  But if you trust them you could certainly keep your funds there, then transfer bitcoins to your everyday account for spending cash.  Kind of like visiting an ATM.