This is a rather large topic, and the exact terminology that should be used (assassination or murder or something else) seems a bit opinion-based to me.
Because of this, I will concentrate on one part of the claim, namely that there may have been a shoot-out between the Black Panthers and the police.
Shots fired during the raid
there were basic discrepancies between the police and Black Panther stories on shots fired
The police as well as the State Attorney gave out incorrect information. There is no evidence that the Black Panthers fired more than one shot. The Chicago Tribune originally published images supposedly showing bullet holes originating from Black Panthers firing at the police, but they turned out to not show bullet holes.
The Tribune itself quickly took back its original claim:
The circles (in the Thursday editions) had in fact been mistakenly put over what appeared to be bullet holes by a Tribune employee acting on information supplied by Policemen
Some of the holes marked by the Tribune In yesterday's late editions as bullet holes may be other types of punctures, officials say Those 'bullet holes' aren't, Chicago Sun-Times
A more recent article by Ted Gregory in the Tribune is more explicit:
The Tribune became part of the uproar when it published a photograph showing holes in a door jamb that it identified as coming from bullets fired from inside the apartment. They proved to be nail heads.The Black Panther Raid and the death of Fred Hampton
Ballistic evidence as presented by FBI examiner Zimmer from the 1979 Court of Appeals case also confirms this:
Countering this defense evidence and in support of their trial testimony in which the survivors denied firing at the raiders, plaintiffs introduced the expert testimony of Robert Zimmers, a ballistics examiner with the FBI crime laboratory. Zimmers also was qualified as an expert to testify regarding the angle a shot entered a surface based on evidence of its impact point. According to his testimony, he examined the weapons seized from the apartment, the shooters' weapons and their bullets, bullet fragments, and shotgun casings and cartridges found in the apartment. He also analyzed impact points on the walls and furniture in the apartment. On the basis of this examination and his analysis, he concluded that there was no evidence of a shotgun blast coming from the corner of the living room where Harris was during the raid. He also concluded that there was no evidence of shotgun shots exiting from the front bedroom where Satchel, Anderson, and Brewer were sleeping, and found no evidence of a shot being fired from within the rear bedroom where Johnson, Hampton, Truelock, and Bell were located.
Zimmers also testified that on the basis of his examination only one shot shell was identified with the seized weapons
Additionally, plaintiffs testified at trial that none of the survivors fired a gun during the raid. And Zimmers' expert testimony corroborated these assertions.
The survivors in this case are all the involved members of the Black Panthers except Hampton (who was sleeping and thus did not fire a shot) and Clark.
Earlier ballistic evidence supporting the police version of events, which was collected by Sadunas, is dismissed as incomplete, either because of Sadunas incompetence or conspiratorial conduct:
There is, however, evidence and reasonable inferences pointing to Sadunas' participation in the post-raid conspiracy. Sadunas' initial ballistics test was incomplete; he compared spent shotshells from the apartment only with the weapons seized at the apartment and ignored the weapons which had been used by the raiders. His examination resulted in a crucial misidentification which would have remained uncorrected absent Zimmers' subsequent tests and conclusions. When he learned of Zimmers' findings, Sadunas retested the shells comparing them with all the weapons including those of the raiders. After these tests, Sadunas readily admitted his mistake. Given this set of events, we think that the determination whether his misidentification was the result of professional incompetence or conspiratorial conduct should have been left for the jury.