1) Maybe monad

  getData :: Maybe Data1
  getMoreData :: Data1 -> Maybe Data2

Note: the monad is probably not just Maybe if it talks to the outside world but more in 2)

List monad

  getData :: [Data1]
  getMoreData :: Data1 -> [Data2]

Dont' know about continuations.

2) There are a few approaches but the most popular are monad transformers, building stacks to combine the effects. For example, to speak with the outside world we need 'IO'. To add failure we might use the Maybe transformer

  MaybeT m a

to build

  type IOMaybe a = MaybeT IO a