a. Do you know what he said to some people in my neighborhood?
This is grammatically correct. That said, while in the correct context this would be an appropriate sentence to say, in many other contexts your use of "some people" could be strangely vague when you would want to be more specific.
Replacing "some" with "certain" will not change this vagueness, but instead draw even more attention to the vagueness, and state that you are intentionally being mysterious. In many situations, being intentionally mysterious is considered extremely rude.
b. I want to know what he said to some people in your neighborhood, because they've started hating me.
This is grammatically correct. It also avoids the (situational) problem in your first sentence, because you are specifying who the "some people" are-- namely, they are the people who now hate you.
Replacing "some" with "certain" now draws clearer attention to the fact that you don't want to name the people in question, probably for reasons of politeness.
c. Do you know what he did to some in his office?
This is technically grammatically correct, but very awkwardly constructed in a way that a native speaker probably wouldn't ever say. The listener will have to ask themselves, "did to some what?" Thinking about it a moment, the listener might conclude that the missing word is very likely "people", but they won't be sure. It could be "Do you know what he did to some furniture in his office?" Or "Do you know what he did to some paperwork in his office?"
Replacing "some" with certain in this sentence would be entirely ungrammatical. This usage of "certain" absolutely requires a following noun, while "some" is allowed to skip this noun in casual speech (but sacrifices specificity in the process, and can be very confusing unless you are certain that the listener understands the correct context).