I never understood the appeal of the pipe operator. It's a kludge to work around the need to eta-expand chained function compositions, which in turn is a kludge to work around the value restriction, which in turn is a kludge to prevent the combination of polymorphism and storage effects from breaking type soundness. Haskell doesn't need any of this.

It's an anonymous function, which it not being called.

Yes, written in pointless style. You could make it less pointless by replacing the (.)s with a point.

    \xs -> take 5 (filter p (drop 3 xs))

https://wiki.haskell.org/Pointfree

Yes. It's three anonymous ("take 5", "filter p" and "drop 3") functions composed by the "." operator, creating another anonymous function.

One of the types, for example:

take :: Int -> [a] -> [a]

What means a function that takes an Int argument and returns another function, that takes a list and returns a list of the same type.

ghci will (usually) tell you:

    phil@arod:~$ ghci
    GHCi, version 7.6.3: http://www.haskell.org/ghc/  :? for help
    Loading package ghc-prim ... linking ... done.
    Loading package integer-gmp ... linking ... done.
    Loading package base ... linking ... done.
    Prelude> :t take 5 . filter (\ _ -> True) . drop 3
    take 5 . filter (\ _ -> True) . drop 3 :: [a] -> [a]

So it’s a function from List of a to List of a