Grammar is just the attempt to codify what already exists in a language and use it as a rule of thumb for creating new text for particular auduiences. Would it be correct to define grammar this way?

There are ways of putting things that reduce ambiguity or make meaning clearer. I'm trying to say that I understand that "grammar" is derived from the language, and so "grammatical mistakes" do not exist in that sense. Perhaps you can say mistakes don't exist because we all make it up as we go along.

I don't know about linguistics, so I don't understand why it should not include discussion of spelling. I find the evolution of languages over time very, very interesting, so I do understand that these are all natual changes and that current meanings and spellings of words are result of those changes.

However, should an English teacher correct grammar or spelling? Should "definate" be marked with a red pen? If not, why not?

When I write something, I try to make the text for the reader (believe it or not), so that it is easier to understand. I also try to use correct spelling. There are obviously differences in "standard" English spelling depending on the version of English you are using, but I try to avoid...mistakes. Obviously, everyone makes mistakes. Maybe I will spell "definite" "correctly", but I'll probably get some other common word wrong.

How is a mistake defined? An "unintentional error"? How do you define "error", when it comes to spelling? Llinguists might allow the existence of "typing mistake" but not "spelling mistake". "Spelling mistake" can be defined perhaps as "an unintentional disagreement with a standard or conventional spelling". It is all relative.

Spelling is certainly a convention. It has become more standardised with printing and with improved communication.

Reading text on the internet inevitably means encountering a fairly wide variaty of backgrounds (people of differnet origins, ages, backgrounds, etc), so it is perfectly understandable that the language is going to have many different forms.

Howver, after emphasising natural changes, relativism, convention, and all those things, I still can't help being bothered by "definate" (for example). It just seems that a teacher with a background in linguistics would never correct anyone's spelling in an English class (or whatever the native language is).