Typeclasses and overloading, what is the connection?

Question

I am currently trying to wrap my head around typeclasses and instances and I don\'t quite understand the point of them yet. I have two questions on the matter so far:

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Answer 1

This only answers question 1 (directly, at least).

The type signature f :: a -> a -> Bool is shorthand for f :: forall a. a -> a -> Bool. f would not truly work for all types a if it only works for as that have (==) defined. This restriction to types that have (==) is expressed using the constraint (Eq a) in f :: forall a. (Eq a) => a -> a -> Bool.

"For all"/universal quantification is at the core of Haskell's (parametric) polymorphism and, among other things, provides the powerful and important properties of parametricity.