I usually see that non-Jewish males are told to wear a kippah or at least a head covering when visiting the Kotel. Is this Halacha? Thank you.
Shalom, Thank you for your question. The laws of wearing a head covering for men (a kippah, or yarmulke) have evolved over time from a practice of the extremely righteous to a general custom of all Jewish men. Covering one's head in synagogue is recorded as a greater obligation, as it is a sign of respect (see Shulchan Aruch 91,3) – but it is unclear if this applies to non-Jews as well. The general practice is to ask all men entering a synagogue (and all the more so, when visiting the kotel) to cover their heads. See for example the book To Pray As A Jew, where he writes "The rule about a head covering in the synagogue should also be observed by non-Jews. The male visitor who does not have a head covering of his own, should take a skullcap provided by the synagogue. the skullcap itself, as I have mentioned, has no intrinsic religious sanctity, but putting in on conforms to the Jewish way of showing respect in a religious setting." (Rabbi Hayim Halevy Donin, To Pray as a Jew, page 60). With all this in mind – the answer to your question as to is this halacha depends by what you mean by halacha. But it is certainly a proper thing to do. Blessings.