1 &3. In this case, the word "want" is definitely a noun, and it means this: : grave and extreme poverty that deprives one of the necessities of life (source: Dictionary and Thesaurus - Merriam-Webster Online)
In other words, people should not suffer from this type of poverty.
2. Yes, after a preposition, you need an object of that preposition, which is a noun. Remember that a gerund is the -ing form of the verb that acts like a noun.
4. That doesn't work. With "freedom of want" it sounds like you have the freedom to want things, and that's not at all the same thing as being from from this feeling of terrible poverty.