Re: Base Throws: Any throw not specified as being a different number is usually 18+
Re: Masterfulness: "Proficiency Rolls" are basically anything that would be a skill check in D&D. The text should call out any proficiency roll as such; off the top of my head, this means craftsdwarfs are really good at using the Heal proficiency to Cure Light Wounds, designing and penetrating disguises, assessing buildings, and determining the magical properities of items by taste.
Re: Theology: You are correct in that there is a dispute between the proficiency text and the craftpriest text. Class features do not count against the proficiencies you may take.
Re: Improving: Most proficiencies, you can invest additional profs in to improve. So if Trapping lets you suceed on an 11+, then taking Trapping a second time would boost it to a 7+. If you do not invest in proficiencies, then they do not improve, and a level 14 god-emperor with healing 1 is exactly as skilled as a 0th level peasant with healing 1.