The use of "real" in the following cases [duplicate]

As intensifiers (words that make an adjective stronger), the adjective form of a word (without the ly) is used very often instead of the adverb form in English. As some of the other answers and comments have remarked, these words are indeed adverbs because they modify adjectives.

For example:

bloody stupid (U.K.),
wicked cold (Boston),
dead certain.

If you said bloodily stupid in England, wickedly cold in Boston, or deadly certain pretty much anywhere, it would sound real funny. People say real hot but don't often say real true, because real is an intensifier in the first but not the second. (See Google Ngram).

There is a comprehensive article looking at various aspects (including historical preferences and shifts) of adverbs-that-resemble-adjectives here; it cites other good sources. The question of which of these so-called flat adverbs are licensed by some style guides is also partially addressed. I'd just add here that sometimes, flat adverbs have a different sense from their related -ly forms:

We went to Rome, and then flew directly on to Rio. (ie as quickly as possible).
We flew direct to Rio. (ie without landing mid-journey).

The use of the -ly-less form is best usually regarded as informal though, in my opinion.

Addressing your second question, I'd reiterate that I think it's about time degree modifiers:

He drove a real(/ly) fast car.
He's plumb loco.
He drove real(/ly) fast.

and other 'secondary modifiers':

It was chillingly realistic.
Time passed excruciatingly slowly.

were recognised as having very different functions from words modifying verbs.