Consider the individuals in George Orwell's "Shooting an Elephant" and Doris Lessing's "No Witchcraft for Sale," who are essentially powerless in their respective societies. How do these individuals behave? What do they do to those who have power in their societies? Why do these people act as they do, and what does their behavior demonstrate about imperialism as a political and social ideology? Use examples from the works in your response.

Ok, so for this question you are considering an important character in "No Witchcraft for Sale" and the minor characters in "Shooting an Elephant." Both stories share a similar imperial setting, with British rulers holding authority and power over the native populations. Orwell's story is told from the first-person perspective, with the narrator being one of the imperialists in control over the people. Lessing's story is told in the third-person, and the imperialists include a white family and white medical professionals, the former of which employs Gideon, an African man from the country.
Orwell's story takes place in Burma, in southeast Asia. Orwell tells the story from his own life, and in the story he, as an imperialist, polices the people who live there. Orwell describes his relationship with the native citizens as:

I was sub-divisional police officer of the town, and in an aimless, petty kind of way anti-European feeling was very bitter. No one had the guts to raise a riot, but if a European woman went through the bazaars alone, somebody would probably spit betel juice over her dress. As a police officer, I was an obvious target and was baited whenever it seemed safe to do so. When a nimble Burman tripped me up on the football field, and the referee (another Burman) looked the other way, the crowd yelled with hideous laughter. This happened more than once. In the end, the sneering yellow faces of young men that met me everywhere, the insults hooted after me when I was at a safe distance, got badly on my nerves.

The people of Burma lash out at those in power. Orwell, being a symbol of the British Empire, receives the brunt of their distaste. The local citizens have almost no authority—even the man who owns the elephant that is shot in the story has little recourse for compensation, despite his elephant not being violent when it was killed.
The people react the way they do—with underhanded actions and taunting—because that is how they can gain agency and power in a structure that gives them none. The people who rebel can choose for themselves, even if it is a small rebellion, when they generally have no choice in the matter, as most things are imposed on them.
To understand how little the people mean to their imperialist oppressors, one need only refer to the following quote, which describes how some of the police officers viewed the death of the elephant after it killed a Burmese man:

The older men said I was right, the younger men said it was a damn shame to shoot an elephant for killing a coolie, because an elephant was worth more than any damn Coringhee coolie.

Orwell shows just how little the English regard the Burmese citizens; their lives are worth nearly nothing. That belief bleeds over into their treatment and is illustrated by the legal status of the Burmese citizens. It is interesting to note that Orwell, despite being in charge, is pressured into shooting the elephant so that he doesn't look like a joke to the Burmese citizens who are watching. Orwell, despite his position of power, feels powerless in the face of their approval.
In "No Witchcraft for Sale," the situation of the Rhodesian cook, Gideon, who serves the Farquars (a white family) is a little bit different. Gideon is very close to the family. He loves their son, who he affectionately calls "little yellow head." In the story, Gideon has a loving relationship with the boy—at times treating him like a friend and at others like a son. Despite Teddy's developing racism, Gideon manages to impart in him some guilt about the way he treats the Africans in the story.
The central part of your question addresses how Gideon saves Teddy's vision with a unique herb, but then refuses—in several different, non-confrontational ways—to give the herb to the white doctors. Gideon saves Teddy's sight because he loves Teddy, but he does not want to sell the secrets of his people/family to the white imperialists to be exploited for profit. The story says:

There was silence after this further explanation, and then Gideon remarked indifferently that he could not remember the root. His face was sullen and hostile, even when he looked at the Farquars, whom he usually treated like old friends. They were beginning to feel annoyed, and this feeling annulled the guilt that had been sprung into life by Gideon's accusing manner. They were beginning to feel that he was unreasonable. But it was at that moment that they all realized he would never give in. The magical drug would remain where it was, unknown and useless except for the tiny scattering of Africans who had the knowledge, natives who might be digging a ditch for the municipality in a ragged shirt and a pair of patched shorts, but who were still born to healing, hereditary healers, being the nephews or sons of the old witch doctors whose ugly masks and bits of bone and all the uncouth properties of magic were the outward signs of real power and wisdom.

The white doctor holds a condescending view—similar to many British citizens—of African natives and their culture: he doesn't think any of the cures will work. He sees the natives as worthless, but the reality stands that Gideon does know a lot about medicine, and he does cure Teddy. His asserts his power (or he reclaims it) by keeping his peoples' secrets. He used it to help, but he would not give it to the white colonizers to pervert.