Yes, it is short for legitimately, and it used like an exaggeration here. We know this person did not really make howling sounds in the theater, but by saying he or she legitimately or truly did it, it intensifies the exaggeration.

This is a very slangy usage of the word "legit." As Jeff says, "legit" is normally short for "legitimate," and it usually occurs in the question "Is this legit?" ("Is this trustworthy/real/not a scam?) It's a slang term that has been around for a long time. The use of "legit" to mean "really"/"actually"/"truly" is very new slang. It's usually used for exaggeration or to make a joke, like Alex says, or to emphasize that something really happened even though it was extremely unlikely ("this guy legit jumped right out of a fourth-story window"). It seems to have become a popular term on the internet over the last couple of years.

It is short for legitimately. It is used just like literally in colloquial English. In spoken English, literally is often used as an exaggeration and has the meaning of figuratively. So legit means figuratively in this sentence. I legit howled in the theater during this death. 3D af. I literally howled in the theater during this death. 3D af. MEANING: I made a sound/outburst/cry that was so intense that it was very similar to a howl in the theater during this death. 3D af. (They did not actually howl)

As Alex said, it is used as a way to exaggerate something. it's used as a way of putting emphasis on something, and is being used as a slang term, or in a way that isn't textbook correct. Jeff has a point that it is not "grammatically correct", but the point isn't to be grammatically correct as much as it is to show that they feel strongly about something.

Not quite right. "Legit" is short for legitimately. "Is this legit?" So the sentence is not grammatically correct.