Morality and its meaning

But as you said in the notebook, if everyone determines their own morality based on their feelings, there will be no objective morality, and that will create the problems that the rabbi pointed out in the notebook.

I am not sure that this is Rav Kook's opinion. See Leaflet I, paragraphs 8,20.

I am far from being an expert on Rav Kook, but he writes this in several places (for example, in his commentary on the Akidah of the Ulat Raya and many others). There are many contradictions in his teachings, especially when it comes to different periods in his life.

1) Does the rabbi believe that it is possible to reach a moral clarification through thought and observation alone?
The questions regarding abortion (at least in early pregnancy), euthanasia, and a few other questions seem unresolved… the feeling is that it is impossible to reach a clear conclusion on the subject, and everyone comes from their own direction…

I don't think this should lead to relativism… there are general issues that all people can agree on… but when you get into the details, there is a limit that cannot be concluded in a normal moral way… and here perhaps there will be room for society and culture to determine (the way in which moral values are implemented and the relationship between them)… is this true…

2) When the sages determined such questions, did they not use their moral reasoning? Isn't determining when a fetus is considered a human being (if at all), and whether a fetus will be considered a non-murderer (which the poskim dealt with), the same question before us? What is their advantage regarding this issue?

1. It is certainly possible that there are questions for which we will not be able to reach a clear answer. This is also the case in halacha, for this there are laws of sufficiency. Therefore, even if you attach morality to halacha, there is no guarantee that you will have clear answers to every question.
And still, everyone should try to reach an answer to the best of their understanding and act accordingly. It is possible that when I am in doubt, society can set standards, although I am not inclined to give society such credit. Even if it sets standards, I do not accept unless I agree.

2. The sages certainly used their reasoning, both in halacha and in morality. But the determination of when a person passes is not necessarily a moral reasoning. It is a meta-moral or meta-halakhic reasoning.
To the best of my judgment, they have no advantage over us in these matters. What is included in halacha is binding (to the extent that the various sources of halacha are binding), and what is not – do as you understand.

When the Torah commands us to “do what is right and good,” it does not specify what that right and good is. Its assumption is that we understand it on our own. In other words, it tells us to trust our moral intuitions. The authority of the sages concerns the law, not the determinations outside the law, such as morality or facts.

But regarding Thou Shalt Not Murder, the same meta-moral and meta-halachic question that faced Chazal also faces my moral questions…
If I accept their determination regarding when the fetus is considered an independent being, it affects my moral decision on the subject, then these are not different questions… It is strange that I accept their determination from a halachic perspective, and from a private moral perspective I do not (in both directions - I can believe more strongly or more strongly)…

Furthermore, in light of the development of science and extensive information regarding the fetus that did not exist in the days of Chazal, we seemingly have a great advantage regarding these determinations.

Their determination regarding the fetus determines the halakhic obligation and has nothing to do with moral determinations. It is possible to be stricter or more lenient. It should be remembered that there is no clear line regarding this, and the determination is somewhat arbitrary. Indeed, you can believe in a positive or negative opinion.
As for science, it has nothing to say on this subject. This is a question of values, not science. But as mentioned, if you think differently, do differently regardless of science.