There are at least two sides to the question: whether the actions are unethical when applied to anyone (not just students), and whether there is an ethical difference when a student is involved.
First, considering the actions when applied to any person, in principle, there is nothing unethical about doing a literature search for someone, nor is there anything unethical about you charging the person to do intellectual work for them. In fact, whether you are paid or not, shouldn't make much of a difference (except for the very important point I make at the very end). Ethical problems would mainly come up when asking if that person credits you for your contribution or not.
If a researcher has someone do some research work for them and then published the work, it is usually considered a professional courtesy to at least acknowledge the other person's contribution, but this is not usually considered an ethical obligation. (Indeed, it would probably be unethical to credit you as a co-author for such little work; see Literature review and authorship).
Second, the fact that the person is a student only really matters if the student intends to submit the work for academic credit. If the student is expected to submit work that they did on their own, then the student would be obligated to report the extent of your assistance to their instructor. Again, whether or not the student paid you is irrelevant--what matters is that the instructor should understand that they received outside help for the work they are submitting.
From your side, it probably isn't strictly required for you to care what the student does with your help. However, if you have reasonable ground to suspect that the student is using your work to cheat on an assignment, then I think you should certainly ask the student to clarify this suspicion. If the student's explanation is acceptable to you, then act as you see fit. However, if you still suspect that the student is cheating, then you should act with the understanding that you are probably collaborating in their cheating.
Ultimately, you should take care of your conscience and act accordingly. And that's where the matter of payment really matters: if the fact that you are being paid makes you less sensitive to your conscience, then you certainly shouldn't receive any payment. Your conscience is worth far more than any monetary price.