An answer to these questions is difficult because there are so many factors that are unknown. What kind of drug is being tested? For what disease or illness? What kind of medical supervision is necessary to ensure safety and relative well being of the study participant? What is the level of risk to the healthy person? Are you looking simply for permission or if this is a mitzvah (an obligation)?
There is some precedent in Jewish text and tradition that helps gauge the response, and allows us to examine both sides of the question. One such example comes from David Ibn Zimri of Egypt in the 16th century, who wrote about the following incident: a government official told a certain Jew to allow his leg to be amputated or else he (the official) would kill another Jew. May this man endanger his life (since the amputation was dangerous) in order to save the life of a fellow Jew? David Ibn Zimri considered this beyond the call of duty (from his responsa, Vol. III, #627).
On the other hand, patients who serve as subjects in experimental therapies are participating in a legitimate medical procedure. Whether the tests succeed or fail to develop a new drug, the patients contribute toward the fulfillment of the goal of medicine as the Torah conceives it: the mitzvah of pikuach nefesh, the saving of life. There is also the mitzvah of rofei cholim (healing the sick).
Therefore, if there is no clear and present danger one could volunteer for a Phase 1 clincal study.
The second question is even more challenging to answer. Certainly the parents would be informed of the medical treatment and would make the best determination for their child, though in the case of a healthy minor I believe it is harder to justify the mitzvah of pikuach nefesh or rofei cholim. I am not sure what circumstances would permit a healthy child to participate in a Phase 1 clinical study.
According to Jewish thought the life of the patient is the primary consideration. Since there in an absence of additional information my reply is on the cautionary side.