Well there isn't just one position an egoist anarchist could take on those examples you gave, so I'll give you a few examples to give you an idea. One position they could take is that they could ignore the situation if it has nothing to do with them or anyone they care about, but if it does have something to do with them or anyone they care about they could concern themselves with the situation (and the specifics of what they would do in response to the situation would depend on the egoist anarchist responding). Now, it is the case that even if it doesn't have anything to do with them or anyone they care about they could if they so desired concern themselves with the situation (and obviously the reasons they are concerning themselves with the situation would depend on the egoist anarchist involved), they could also (and this could relate to that last one) pretend to concern themselves or not concern themselves with the situation if it in some way benefits them (and of course there is no objective idea of what benefits an egoist anarchist and so that is left completely to the individual egoist). There are also Egoist anarchist who have desired to either destroy this way of life (State, Capitalism, Society, Civilization, etc) or if they didn't think that was very likely they desired to live in an intense conflictual way with this world (because they despised this way of life) and either of these two camps might concern themselves with those situations or not depending they want to, if they decide to they might in some way attack some manifestation of those situations (the school, the individuals who control the resources, the hospital, the doctor, etc) or they could partake in some other venture against those situations if they wanted to. Not all of these positions are mutually exclusive, and of course there are probably more positions an egoist anarchist could take that I have not thought of while writing this.
The purpose of that tedious list of positions that an egoist anarchist could take was to show that Egoist anarchism is very open ended and that it is very hard to pinpoint what any specific egoist anarchist would do in any given situation. Also it makes sense to say that there is also not only one type of egoist anarchism, there have always been many expressions of it. Now, I don't want to describe all of the specific egoist anarchisms that have existed in detail, but I can give you names of the various egoist anarchists so you can see for yourself the various manifestations of it, John Henry Mackay, Benjamin Tucker, John Beverley Robinson, Émile Armand, Miguel Giménez Igualada, James L. Walker, Renzo Novatore, Bruno Filippi, Enzo Martucci (also went by Enzo da Villafiore, Lev Chernyi, early S.E. Parker (later on he changed his position to an egoist Archist, which is the exact opposite of egoist anarchist), the Bonnot Gang and other Illegalists, Enrico Arrigoni (also went by Frank Brand), Alfredo M. Bonanno, Feral faun/Wolfi Landstreicher/apio ludd (pseudonyms of the same person), and I'm sure there are others in which I forgot or who i don't know about. There is obliviously qualities all versions of it have shared, such as rejection of the state, religion, morality, society, obligations, fixed ideas (ideologies), etc and the pursuit of what Stirner calls Owness making ones life ones own despite of all the claims made against it, but the way this manifests and how each egoist anarchist has decided exist in and against this world is unique to each individual.