> 1. How would I convert capital letters into small letters?
>
> 2. How would I remove vowels from a string?

I expect the first problem is actually to convert the upper case letters in a string to lower case, as the single-character version isn't a very interesting problem.

A little thought shows that the first problem can be expressed as both a catamorphism or an anamorphism.  The anamorphic solution would be [(p,f)] where

    p as = as == [] and
    f (a:as) = (makeLowerCase a, bs).

The solution to the second problem is clearly a catamorphism, and one solution might be (|[],g|) where
    g (a:as) = if isVowel a then as else a:as

The definitions of 'makeLowerCase' and 'isVowel' are quite simple (assuming English/Ascii, as pointed out in other messages), while finding the prelude functions for the patterns of recursion might take a little more thought.   Suitable, possible, as homework questions in an introductory Haskell course ...

Robin