Because hurt is a verb there, technically it's the adverb. I would probably only use hurt bad if that was the character's voice. But if you use hurt as a noun, it can be a bad hurt. Then there's the object: with, 'don't feel bad' bad is the object, not an adverb of feel.
Yes. I'm thinking in the context it's best with the adverb badly. I'm probably making more of it because I can get paranoid about using an adverb when actually they are necessary. Necessary evils - lol.
'hurt bad' is poor grammar, but many people say that, so it's ok to use it in dialog, but not in narrative, unless the narrator uses poor grammar consistently for some good reason... 'badly hurt' could be ok or awkward re syntax, depending on the context, though correct grammar... 'hurt badly' is correct grammar, but again, whether it reads well depends on the context...
Moreover, I do not think the word "bad" can be used in the context of emotion, because the word itself is inherently not emotive. If I say, "I feel badly," it technically means that I am not good at feeling; or in other words, I felt, but I did it poorly. If I say that I feel "bad," then I am using an adjective to describe a verb, albeit a state-of-being-verb. That said, "hurt" is a verb, and once again, the fact that it is a state-of-being-verb makes people confuse it intuitively with a noun. Saying I was "hurt bad" could be alternatively written, "My hurt was bad," since we're using "hurt" as a noun, writing it this way demonstrates the error. Saying you were hurt "badly," once again, implies that the guy hurting you did a poor job. A better word in this context would be severely, or even greatly. Of course, if the word "bad" can also mean, "to a great extent," then half of my argument is incorrect.
It's quite simple. It ultimately depends on how it's being used. I agree with @mammamaia re: not using it in narrative, however I would add to that to say you can use it not just with dialog but also a characters internal workings. Meaning He watched her grit her teeth. Looked like it hurt bad. This is fine, however this gives your character this 'voice' because it's a style of voice. For me personally I would say It hurts so bad, rather than It hurts a lot.
sure, your narrator can have voice in first person... but if you use poor grammar here, she should be consistently 'casual' or it'll stick out like a sore thumb...
It is if The People accord that it is. The meaning of any word is arbitrary and unfixed, tied only to a group decision accorded by those making use of the word and these accords change all the time. Linguistically, this is a defining part of a true language. This is what distinguishes a human language word from the sounds made by higher primates, the meanings of which we have deciphered, but which are hardwired and not group decision. If a spider monkey makes a certain sound when danger is from the ground as opposed to from the air (and they do), the sound is hardwired and fixed in all howler monkeys across all areas of howler monkey population, whether there is contact or not, one group with another group. Human words are not like that. The Castellano group has decided that the four legged animal we enjoy having around is to be called a perro. The English group has decided a different word, dog. It may seem to mean this from a purely analytical approach to the syntax, but no person means that when they issue that word grouping. The person who issues those words is expressing the experience of an unpleasant or sad emotion or unpleasant physical sensation. Were I to say I feel badly for him, I am not expressing the sentiment that as the individual's representative I am doing a poor job at the experiencing of emotion, though logical review of the syntax might come to that conclusion. It means I have pity for him. But feel is not a copula verb. Instead, bad in this context belongs to an elided and nested prepositional phrase. I am in (a state of (bad feeling)). No, it is not a copula verb being confused for a noun. This and the next example you are about to give are not state-of-being verbs (copula) but past participles, which is verb serving as adjective. I was hurt bad. Was is a copula verb, and unique to the copula verbs, the modifier is an adjective, not an adverb like all other verbs take. Hence, here hurt is a past participle of the verb to hurt. It cannot be traded with a noun for logical or syntactic comparison. Past participles are verbs serving as an adjective because the result of the action causes a quality and qualities are expressed through adjectives and adverbs, in this case an adjective because the verb being modified is a copula, was. Only if one takes an over-literal view of the syntax.
"Only if one takes an over-literal view of the syntax." I think one should always start from a literal perspective and work therefrom. If the person writing wants to disobey the rules, then he should at least know them first, right? Anyway, check this: http://data.grammarbook.com/blog/definitions/bad-vs-badly/ According to that, you would "feel bad," not "badly," so I am correct (according to this site) in that regard; yet, I still disagree intuitively, but that's because some of what I know is self-taught, and the English language has rules that are, as you would probably agree, inconsistent or unable to account for all words or phrases. This is like having a discussion about why we put prepositions at the end of many verbs: Check this out (I can't just check it?) Sit down (I think I'll sit up, thank you) Fell down (Fell up?) Fell asleep (Not a preposition, but could we not just write "sleep" as an imperative?) My point is that I hope the original poster has learned his lesson about posting grammatical questions. : D