For now Mist requires a full blockchain but we already started testing a light-client on the node that would avoid that.

Not all app need to show ether to the user, but that is the currency used to pay miners for transaction fees. There are ways in which the app developer can try to abstract the concept of ether using other currency, or even subsidising the users by paying their cost via other means (like what digix gold does).

Ether is not used as a reward for hosting the app, but for changing saving data and changing states on the blockchain. We will have a P2P solution where users are paid to host actual application files.