In matters of worship the Imām was at his most careful and his sharpest. And not without good reason, the scholars settled on giving fatwā in ʿibādāt by his view.
This comes from looking across the cases and seeing the pattern hold. It stands as long as there is no report from the Imām himself agreeing with the other side. Two examples: whether water already used for wuḍūʾ is still pure, and doing tayammum when the only liquid you can find besides water is nabīdh made from date pits.
In matters to do with the courts, the fatwā follows Abū Yūsuf's view. The reason is experience. He sat as a judge, and doing the work taught him things the others had never run into.
Here is a case that shows the same idea working, even though it is not about Abū Yūsuf (d. 182H) or about the courts. Abū Ḥanīfa (d. 150H) once held that giving charity is better than a voluntary ḥajj. Then he performed ḥajj himself, felt how hard it was, and took his earlier view back. Doing a thing can change a jurist's judgement about it.
The fatwā follows Muḥammad's view in all questions of inheriting through dhawī al-arḥām, the relatives who inherit through a female link. But read the rest of the sentence carefully, because it changes what this rule is. Ibn ʿĀbidīn quotes Sakb al-Anhur saying that Muḥammad's view here is also the better known of two reports from Abū Ḥanīfa (d. 150H) himself. So Muḥammad is not overruling the Imām here. The two of them agree. That makes this rule quite different from rule 2, where Abū Yūsuf really does take over a whole subject.
When a question has both a qiyās answer and an istiḥsān answer, you take the istiḥsān one. There are exceptions, about eleven of them according to Ajnās al-Nāṭifī.
Najm al-Dīn al-Nasafī (d. 537H) counted more, and brought the number of exceptions up to twenty two.
Fakhr al-Islām al-Bazdawī defines istiḥsān like this. You have a question that looks like a whole family of other questions. Qiyās would hand it the same ruling they all get. Istiḥsān is stepping away from that ruling to a different one, because there is a reason that makes stepping away the stronger course.
It comes in three kinds. First, istiḥsān because a text says so: salam, ijāra and qarḍ all run against strict qiyās, and are allowed because a text permits them. Second, istiḥsān because the scholars agreed: istisnāʿ, ordering something to be made, is allowed even though at root it is selling a thing that does not exist yet. Third, istiḥsān out of necessity, to keep hardship off people: small ponds and wells count as pure, and people are excused for splashes of urine, for muddy roads, and for small unfairness in price in everyday dealings.
Anything outside ẓāhir al-riwāya counts as weak. The one exception is where the mashāyikh have plainly declared sound a view that goes against it.
Al-Ṭarsūsī (d. 758H) states it for judges: a judge who is a follower may not rule by anything except ẓāhir al-riwāya. Not by the rare report, unless the scholars say plainly that fatwā rests on it.
One addition. If a question is not dealt with in ẓāhir al-riwāya at all, but is settled in some other report, then you follow that other report.
When two proofs clash and one of them shows itself to be the stronger, you must act on that one, and the weaker one drops out.
Declaring someone a disbeliever is a very grave step. So the rule is this: I will not call a believer a disbeliever as long as I can find any report saying he is not one. Even a weak report is enough to hold me back.
Once a mujtahid takes a view back, it is no longer his position. You then have to go and find the view he moved TO, and act on that one instead. The first view is treated like a ruling that has been cancelled. Note this is the third place the map says "later beats earlier": see also the order the six books were written in, branch 5, and the Imām's two conflicting views, branch 6.
If you know which view came later, that later one is his madhhab, and the earlier one counts as cancelled. If you do not know which came later, then neither one is judged to have been taken back in favour of the other.
The men who wrote the mutūn, the main texts, bound themselves to putting only the sound view in them. So if some other book says something that clashes with a matn, that other book does not win. There is one exception, and it matters. If the other book plainly declares its own view to be the sound one, then it does win. A stated taṣḥīḥ beats one that is only implied by where a view happens to sit.