As far as observation goes, it really depends on what is being observed.
No it doesn't. Our observation is just an experiences, and experiences are
always subjective. At least per the more strict understanding of objectivity as predominantly used in philosophy.
However, we might (subjectively) observe a subject-independent phenomenon.
If you observe that you feel hungry, that's a subjective observation. If you observe that the moon is in its waxing gibbous phase, that is objective.
No, this confuses what is subjective and objective. The objective thing is what exists independent of a subject. An observation is not independent of a subject (e.g. perspective). But
what is observed might also exist independently from any subject. And hence the observation itself is subjective, and
always subjective, but
what we observe might be independent.
So in your example, the
observation of the moon is subjective. The
moon itself is objective. Don't confuse the observation for the thing itself.
The difference is that other people can confirm your objective experiences, whereas nobody has access to your subjective experiences.
Since this is the philosophy forum, we should be using terms as understood in philosophy, and "objective" means "independent of any particular subject's perspective, attitude, experience etc". Since vision is an experience, and what one observes is very much dependent upon perspective, an observation itself is
always subjective.
In philosophy, therefore, "objective experience" is an oxymoron.
In science, or psychology, they may use the weaker notion of "objectivity" that you are trying to use, but, strictly, this being the "general philosophy" forum, you should probably use the stricter understanding.
Every individual has their own subjective experience. However, facts about the world that everyone can observe independently and agree on (in principle) are objective.
Yes, the "facts" are objective. But an observation of the fact is still subjective. The moon can be taken as objective. But an observation of the moon is not the moon. The moon is objective, whereas the
experience of the moon, the observation etc, is subjective.
Science views objectivity differently. It doesn't really use the idea of subjective experiences at all, but rather refers to the idea of "observer-involving" measurements (that are also publicly accessible). I think it's gone down this route since the discovery of QM, and the impact that observations can have at that level. Anyhoo - science takes these "observer-involving" measurements and infers the objective features of the phenomenon, i.e. those that are subject-independent.
But this is the philosophy forum.