Wearing no head-covering?

Question

Under what circumstances is it permissible for a man to wear no head-covering?

If one is in a place that is experiencing anti-semitism, for example, does one need to wear a hat if one feels endangered wearing a Kippah? What if it is culturally offensive to wear a hat - say, indoors, or meeting an important person?

Does it make a difference if one is seated? On that note, may one eat (or for that matter make a Berachah) without a head-covering in such a case?

(If this is too broad, I can break it up into smaller questions, but I think the questions are interrelated enough to keep together.)

Answer 1

The footnote to Mishnah Brurah 2:12 says that in a place where the law is to go (he says go, not sit) bareheaded in front of officers, you must follow it.

When sitting inside, there is room to be lenient in a time of need (Beer Heitev 2:6). I heard in the name of the Bach that wearing a kipah is a midas chasidus but not required, and if so, there is a lot more room to be lenient.

(I forgot to add this, so I edited it in.) The BH"T writes there that to mention Hashem's name is forbidden, but in a time of need he can cover his head with his hand; see there. The M"B 2:12 writes that it is better to just cover his head with his sleeve and then it is a fully satisfactory covering.