What is the central conflict of "Sredni Vashtar" by Saki? Who took part in it? Was there a resolution to the conflict?

The main conflict in "Sredni Vashtar" is between the protagonist Conradin and his cousin Mrs. De Ropp, the antagonist. For Conradin,

[Mrs. De Ropp] represented those three-fifths of the world that are necessary and disagreeable and real.

His cousin and guardian, Mrs. De Ropp seems to delight in the fact that Conradin is a sickly child who cannot do the things that ordinary boys can, for then she can impose her will upon him. Fortunately for Conradin, he has an imagination that is "rampant under the spur of loneliness"; indeed, it is this creativity which keeps the boy alive longer than the doctor has predicted.
Each day, Conradin's goal is to enjoy himself and thwart the Woman's, as he calls her, attempts to spoil his pleasure. He does this by avoiding the gardens where a window can easily open and from which scoldings issue forth. Instead, Conradin directs his attention to a certain old tool-shed that is almost hidden behind overgrown shrubbery. Inside this old shed, Conradin has found a haven, "something that took on the varying aspects of a playroom and a cathedral." There are multitudes of imaginary figures, issuing from Conradin's reading and his own imagination. In a far corner, however, there are two living creatures: a Houdan hen upon which Conradin lavishes much attention as well as his devoted affection, which has no other outlet. Also, in a far corner Conradin has a large ferret which the butcher boy has smuggled in for him. This sharp-fanged "polecat" incites fear in Conradin, but he views it as a mysterious little deity and names it Sredni Vashtar.
After the "Woman," as Conradin thinks of her, discovers that he has housed the little hen in the tool-shed, she removes the beloved hen and sells it. Happily, she informs Conradin that the hen is gone because it was not good for him to "be pottering down there in all weathers." After she says these words,

[With] her short-sighted eyes she peered at Conradin, waiting for an outbreak of rage and sorrow, which she was ready to rebuke with a flow of excellent precepts and reasoning.

However, Conradin remains stoic, even when she troubles herself to make toast for tea time.

"I thought you liked toast," she exclaimed, with an injured air, observing that he did not touch it.
"Sometimes," said Conradin.

Later, however, in his suffering of the loss of the only creature that he has had to love, Conradin prays privately to Sredni Vashtar, "Do one thing for me." Feeling that the god should know what he means, Conradin mentions nothing; he only chokes back a sob as he glances at the empty corner where his hen used to be. The next night and every night afterwards, Conradin prays to Sredni Vashtar.Then one day, the Woman informs Conradin that she has noticed that he still goes to the tool-shed. When Mrs. De Ropp goes out to the shed, Conradin imagines that she will open the cage and peer in with her myopic eyes. "And Conradin fervently breathed his prayer for the last time" as he watches out a window.
After some time, Conradin begins to despair. A maid passes under the window on her way to make tea inside. Then,

...out through that doorway came a long, low, yellow-and-brown beast, with eyes a-blink at the waning daylight, and dark wet stains around the fur of jaws and throat. Conradin dropped on his knees.

"Tea is ready," the surly maid calls, then asks, "Where is the mistress?" Conradin simply replies that she has gone to the tool-shed. This time the toast tastes delicious to Conradin, and he delights in it. 
After a while, Conradin hears the maid scream. Then another asks,

"Whoever will break it to the poor child? I couldn't for the life of me!" exclaimed a shrill voice.

And while the servants debated the matter among themselves, Conradin simply made himself another piece of victory toast.