That's my biggest question of the whole series in fact. 

Its constantly mentioned how any use of Malfeasance could lead to being burned as it did 300 years ago, 

Hopefully Kvothe will have learned the name of fire by then. 

I think it should. That's pure malfeasance, and he did it in front of other people. If they knew at the University what he had done, he would at least be expelled.

The only witnesses are his team and potential bandit survivors, and thye face the maer justice if they come forward. His team would never testify against him, he saved their lives. Also, strickly speaking, who claims the eld, that might be a political issue. WOuld the remains even show malfeasance?

- Vint is a highly superstitious country, they wouldn't even want to talk about "magic", much less mess with magic users.

- His team are the only witnesses, and they wouldn't testify against him, because he saved their lives

- He used naming, not sympathy (according to the stories, not what really happened), so they would have to prove he knew the names of fire and lightning. 

Is using magic in self defence allowed? We know using magic to harm is forbidden, but what if there are allowances for self defence?

As far as the stories about Kvothe go, he has demon blood; he can see in the dark; he sleeps an hour each night; when the moon is full he talks in his sleep in a language no one can understand; he laid with Felurian, getting gifts from her before escaping from the Fae (wow, this one is actually true!); he doesn't bleed; he can conjure/invoke demons; etc.

The teachers know this is all just stories, with no truth to it. He himself says his stories grew bigger from Vintas to the University, how he actually rescued girls from shamble-men, Adem mercenaries, an ogre or two or even a trow instead of pretenders posing as Ruh, how he invoked fire and lightning like Taborlin the Great, while the teachers know for a fact he is still stumbling trying to grasp the Name of the Wind, so that he wouldn't know both the Name of Fire and Lightning on his travels...

And, as said before, anyone who described it would describe as if he invoked Fire and Lightning like Taborlin the Great, so this would make the story even the more unbelievable for his teachers (except maybe Elodin, Elodin surely knows Kvothe is true to the legend, having brought a Shaed from the Fae, sewn by Felurian herself).

So, yeah, even if the stories reached the Masters ears, even if those who saved him actually told the stories around, even if everyone 'knew' he practiced malfesance, it would still not be enough to convict him, it's not like with Ambrose, where there were witness. His witness were a few bandits and a mercenary group that thinks Taborlin the Great was reincarnated on the boy and slept with Felurian, they surely must be out of their minds :p

THe only reason the trial occured is that there were many nobles to back up the claim. Unless anoth noble or priest stands as a witness, no issue will be raised.

But didnt Hemme (the master who hates him) just get promoted? So surely he would have the power (and will) to expel Kvothe for Malfeaseance. Even if it did seem like just a crazy rumor didnt they mention how the university is very protective of it's reputation? I think they will expel him because his rep is giving the university a bad name - teaching 'dangerous' magic etc.

the good thing is university discipline is decided by a vote by the masters, and most are favourable to kvothe if he at least toes the line.