Yes she was. Because he thought it was a "proper" Temple that would get rid of her "adulterous ways" but really it's a sex cult that allows her sexual freedom.
True but I very much doubt that Ziva punishes her too badly. Qeteshians are all about sexual freedom, pleasure & ecstasy. She wouldn't do anything to make Alice feel bad or too make her want to leave. Caleah may do chores as well but it's a small thing to do when u can have all the d*** ye want from the Priest of QC

also I doubt she will have to break up with MC just because she joins officially because she enjoys sex & u r a priest. Once we start knocking up priestesses, I reckon the status que of the Temple will forever be rocked.