Q. 1) If someone calls Hatzalah on Shabbos and then it turns out that everything is fine (for example a child choking and the food comes out), should he call back hatzalah to cancel the call?…
A. Some physicians recommend to have the child checked medically anyway, as other unseen damage may have occurred.
Horav Shlomo Miller’s Shlit’a opinion is that it is highly likely that by the time he is able to call back, the Hatzalah team has already been dispatched and they are about to arrive. Add other multiple variables such as the number of calls usually expected during a regular Shabbos and the need for the availability of responders, the instructions given to the dispatcher of this particular Hatzalah team, etc., it is best not to call back, or at least if deemed necessary, to call back with a shinui, (change) or by asking a Gentile to call back.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a