The grammar in the English novel Forrest Gump

I am currently reading the English novel Forrest Gump and this is the first time I am reading a novel using my second language.
I realized that the author is writing somehow different from the English I learned at school,
for example he spells wile for while, nex for next, sposed for supposed, cept for except, axe for ask.

My questions are:

1. Is this grammatically correct?
2. Since this is the only English novel I have finished so far, is this style of writing common in English literature?
3. What is author’s intention for using spelling like this?