For the record I'll document the identifications of the three stories made in the comments. I have made this a community wiki answer so please feel free to update/correct it as necessary.
The first story is Black Destroyer by A. E. Van Vogt. The creature is called Coeurl and is the last of its kind on a desert planet. It feeds by extracting a chemical from the creatures it kills. In the original story this was phosphorus, though when the story was included in the fix-up novel The Voyage of the Space Beagle this was changed to potassium. The humans trick Coeurl by stopping their ship instantly then approaching Coeurl so their ship looks like Coeurl's home star. Coeurl commits suicide when it realises it is doomed.
The second story is from Joe Haldeman's Forever War series. It could be an excerpt from one of the novels, or it could be the novella End Game published in 1975, which has an extended sequence of actual melee combat in the stasis field, punctuated by a nova bomb. This contains the scene mentioned in a comment where a quarterstaff is poked through the statis field and becomes red hot:
I took one of the quarter staffs down to the edge of the field and poked it through, a centimeter or so. When I drew it back. the point was melted off. When I showed it to Charlie, he just rocked back and forth (the only way you can nod in a suit); this sort of thing had happened before, one of the first times the stasis field hadn't worked. They simply saturated it with laser fire and waited for us to go stir-crazy and tum off the generator. They were probably sitting in their ships playing the Tauran equivalent of pinochle .
The third story could be The Mutant Weapon by Murray Leinster, which is part of his Med Ship series. The creature is called Murgatroyd:
Murgatroyd was the tormal member of the Aesclipus Twenty’s crew. During three weeks of overdrive travel he was his normal self. He was a furry, companionable small animal who adored Calhoun, coffee, and pretending to be human, in that order. Calhoun traveled among the stars on professional errands, and Murgatroyd was perfectly happy to be with him. His tribe had been discovered on one of the Deneb planets; their charming personalities made them prized as pets. A long while ago it had been noticed that they were never sick. Then it developed that if they were exposed to any specific disease, they instantly manufactured overwhelming quantities of antibody for that infection. Now it was standard Med Service procedure to call on them for this special gift. When a new strain or a novel variety of disease-producing germ appeared, a tormal was exposed to it. They immediately made a suitable antibody, the Med Service isolated it, analyzed its molecular structure, and synthesized it. So far there hadn’t been a single failure. So tormals were highly valued members of Med Ship crews.
In particular, The Mutant Weapon contains the text:
The tormal wriggled as Calhoun made the injection. But it did not hurt. There was an insensitive spot on his flank where the pain-nerves had been blocked off before he was a week old.
However all three of these are really novellas rather than short stories so including them would make for a long anthology. Also there is no anthology containing all three listed on the ISFDB. This makes it sound like you might have read an unauthorised collection.
