Haskell curried function types

Question

I'm a little confused by types returned by curry and uncurry functions:

Prelude> let pairMax (a,b) = if a > b then a else b
Prelude> :t pairMax
pairMax :: Ord a => (a, a) -> a
Prelude> let pairMaxCurried = curry pairMax
Prelude> :t pairMaxCurried 
pairMaxCurried :: () -> () -> ()

I don't understand why the curried function's type consists only of Unit types. Trying to apply pairMaxCurried unsurprisingly results in an error:

Prelude> pairMaxCurried 1 2

<interactive>:10:16:
    No instance for (Num ()) arising from the literal `1'
    Possible fix: add an instance declaration for (Num ())
    In the first argument of `pairMaxCurried', namely `1'
    In the expression: pairMaxCurried 1 2
    In an equation for `it': it = pairMaxCurried 1 2

while currying and applying in the same line is fine:

Prelude> (curry pairMax) 1 2
2

The same goes for uncurry:

Prelude> let twoMax a b = if a > b then a else b
Prelude> :t twoMax
twoMax :: Ord a => a -> a -> a
Prelude> let twoMaxUncurried = uncurry twoMax
Prelude> :t twoMaxUncurried
twoMaxUncurried :: ((), ()) -> ()

Declaring explicit type doesn't help:

Prelude> let pairMaxCurried = (curry pairMax) :: Ord a => a -> a -> a
Prelude> :t pairMaxCurried 
pairMaxCurried :: () -> () -> ()

Question 1. Why is the type not correctly inferred?

Question 2. Is there a way to bind curried/uncurried function to a name while preserving the correct type?