It is important to know that a fatwa in Islam is a legal ruling. During the time of the Prophet ﷺ, seeking a fatwa was addressed directly through revelation, as in the case when the Prophet ﷺ was approached about a ruling on inheritance:
يَسْتَفْتُونَكَ قُلِ اللَّهُ يُفْتِيكُمْ فِي الْكَلَالَةِ
They request from you a [legal] ruling. Say, "Allah gives you a ruling concerning one having neither descendants nor ascendants [as heirs]."
— Surat An-Nisa 4:176
Or when the Prophet ﷺ was asked about guardians marrying orphan girls:
وَيَسْتَفْتُونَكَ فِي النِّسَاءِ قُلِ اللَّهُ يُفْتِيكُمْ فِيهِنَّ
And they request from you, [O Muhammad], a [legal] ruling concerning women. Say, "Allah gives you a ruling about them"
— Surat An-Nisa 4:127
As can be seen from the above verses, a fatwa is a legal ruling, with the governing law being the Islamic jurisprudence. It may go beyond a simple question-and-answer setup.
Your post: Are there modern-day fatawa which say "I don't know" or words to that effect?
Yes, but they are not typically published. Responding with "I don't know" has been common over the years since the death of the Prophet ﷺ as documented by An-Nawawi in his book Adāb al-Fatwa wa al-Mufti wa al-Mustafti about the companions:
وروينا عن عبد الرحمن ابن أبي ليلى قال أدركت عشرين ومئة من الأنصار من أصحاب رسول الله صلى الله عليه وسلم يسأل أحدهم عن المسألة فيردها هذا إلى هذا وهذا إلى هذا حتى ترجع إلى الأول
NOTE. My own translation, so treat with care.
We were told through 'Abdur-Rahmān ibn Abi Layla that he said: "I have seen 120 from al-Ansār from the companions of the Messenger of Allah ﷺ where one would be asked about a matter that he would refer to another companion, and this would go on until the matter returns to the first companion.
— Adāb al-Fatwa wa al-Mufti wa al-Mustafti, pp. 14
In the same book, An-Nawawi mentioned the same attitude by the following generations:
وعن الشعبي والحسن وأبي حصين بفتح الحاء التابعيين قالوا إن أحدكم ليفتي في المسألة ولو وردت على عمر بن الخطاب رضي الله عنه لجمع لها أهل بدر
NOTE. My own translation, so treat with care.
Through Ash-Sha'bi and Al-Hassan and Abi Hassīn (from the tabi'is) said (addressing other tabi'is): "One of you gets asked about a matter and issues a fatwa that had it been 'Umar ibn al-Khattāb who was asked about such matter, he would have gathered for it the companions who witnessed [Battle of] Badr [the ones with the highest level of knowledge among the companions].
— Adāb al-Fatwa wa al-Mufti wa al-Mustafti, pp. 15
The closest analogy to modern-day terms, a mufti at the level of a mujtahid (the top two levels as per "What are the minimum requirements for someone to be a student of knowledge?") is a lawmaker, but the law passed is not legally binding as it may not have a binding execution portion (unlike a ruling coming from a judge where the ruling has to have an execution portion). This is the meaning of the quote you mentioned:
Abu Hanifa (R.A.) is reported to have claimed: "we [the jurists] realize that this is merely an opinion; yet, it is the best we have been able to reach. If someone produces an opinion better than this, we will accept it".
Sometimes a fatwa will result from a mere question (no further action may be required), whereas a judge's ruling will result from litigation and further action will almost certainly be required.
Your post: One thing I rarely see (maybe never see) in modern-day fatawa is an indication of doubt in their ruling.
A fatwa would only get published when the team working on it are confident that the opinion expressed is the one to which they subscribe.
Your post: This fatwa does not mention the different views on oral sex (which I surveyed in this answer), nor the different views on semen being impure (FatwaIslam says semen is clean).
A fatwa is considered maqām hukm (a setting of issuing a law), which is typically issued by a mufti (jurist). A fatwa, by definition, should have only one clear direction.
When, however, the matter under investigation is being studied, then all sorts of different views are considered. This is maqām tashāwur (a setting of deliberation or consultation) before issuing a response to a fatwa. In a university setting, which is maqām 'ilm (a setting of studying, as in books or sittings or lectures that discuss the principles of jurisprudence), not only would all the views be considered, but also the reasoning behind why each imam selected one view over another.
In the case of one fatwa that I witnessed, one of the scholars gave a hard time to another on the committee since he had spoken with an opinion without knowledge of all the different possibilities (12 in total, and he voiced the opinion of 11 before giving his opinion on the matter: opinions of the four imams, opinions of the early scholars of each school, and opinions of the late scholars of each school). In the end, the fatwa showed only one view.