Good discussion here. I have pondered the same issues, and sort of filed them away in the back of my mind.
I have tended to translate saddha / shraddha 信 as trust, a tentative belief in something without understanding, because it appears to be credible. This would be the resolution of suspicious doubts that hinder our practice.
I came across three Chinese translations of pasada / prasada. Pure faith 淨信 Sincere faith 信心 Confident faith 信受
I gather that pasada, In the Nikayas, is Gotama's resolution of samvega 厭怖. Samvega was his state of mind after his first three encounters. Pasada was his mental state after the 4th encounter.
I saw adhimutti / adhimukti 信解 as joyful faith, kind of an aha! moment. I have seen the Pali wprd adhimutti translated as disposition or resolution.
adhimokkha / adhimoksha 勝解 seems to mean decision, coming to a determination. In more casual use, it sometimes appears to be a synonym for adhimukti.
There is also the Pali word adhitthana 受持, one of the ten paramis of Theravada; which seems to mean determination or 'standing up'. Adhisthana 地瑟娓曩 or 加持 might be the same word in Sanskrit, but appears to have a much different nuance, and is translated as assistance, blessing, empowerment, or initiation. Also, blessing here seems to be used in a different sense than benefit or blessing as merit (punna / punya 功祚) or merit & virtue (punya & guna 功德).
One of my issues is I want Buddhist terms to have consistent fixed meanings in every context. That does not always happen. Several different words can be exact synonyms is some contexts, but have specific meanings in others. The specific nuances are not always consistent either. Then rendering them into English can further cloud the issue.