I haven’t learned the Rambam recently, and the concept is complex, but from my memory, this is how I understand it:
The primary definition of Chillul Hashem is to commit an aveira intentionally. If this were done in front of a minyan of Jews (as DH mentions), it would be Chillul Hashem in public. That would be a Chillul Hashem according to all opinions.
Additionally there is a secondary aspect to Chillul Hashem which is when someone acts in a way that decreases Hashem’s Kovod in the world. This is understood as to mean if someone acts in a way that is not befitting to him. He is doing something that is not perfectly right. I believe there is somewhat of a machlokes if this only applies when doing something objectively morally wrong, or even if it is only wrong because people expect more of that individual (i.e. the world holds Jews to a higher standard — perhaps due to antisemitism and they’re looking for problems, perhaps because they instinctively understand we have more obligations then them — either way if your action would be unbefitting to their perception of how you should behave)
Finally there is the general conept of “yehi shem shamayim misahev al yadcha”, that a person has an obligation to make Hashem “loved” through his actions, and that people should say “fortunate is one who teaches his child Torah”. Colloquially this concept has also been lumped under the concepts of Kiddush Hashem/ Chillul Hashem, although I’m not sure it’s technically the same mitzva.
So to apply to the above examples:
If something is a Mitzva, by definition it is a Kiddush Hashem to do it, not a Chillul Hashem. If something is an aveira, it is a Chillul Hashem (My understanding is that in addition to the aveira itself, if an aveira is done intentionally, there is also an aveira of Chillul Hashem. This can be in public or private –Pirkei avos discusses one is mechallel Hashem in private — although not all meforshim interpret it that way). The class trip/ telling kids to behave extra well probably falls under the third concept of causing others to say “fortunate are those who study Torah”, as may the messy house example. However for it to be Chillul Hashem there must be something wrong about it, either objectively or on a certain level. If something is completely fine to do, but bothers others for unreasonable reasons, there is no inyun of Chillul Hashem, even if the person gets upset a Jews as a result.
tro11 – This somewhat addresses your issue. The point is not what people say/ think about Jews. It is our obligation not to do anything wrong that will cause that diminishing of Kovod Hashem in the world. If your actions are not wrong, no issue. If they are somewhat wrong (being rude, cutting people off), it may fall under this concept according to the opinions that it would apply even if the “wrongdoing” is only due to higher expectations.