These are great questions, Grace! Regarding your question as to why there would be a point in having people “convert” if they do not practise privately or believe it in their hearts, I have some speculations as a history major who has learned a little bit about Inquisitorial approaches to religious deviancy. These institutions functioned as much for social control as they did for (supposedly) ensuring the salvation of the souls they governed. Whether the pendulum swung one way or the other depended on the personal motivations of the many individuals that comprised these institutions, and that is unfortunately difficult to tell without something like preserved diaries from all of them.
As far as the effects go, Inquisitions functioned–regardless of the motivations of the inquisitors–as a deterrent. Prosecuting, torturing, imprisoning and sometimes executing people for having unorthodox beliefs sends a message to the population to at least pretend to be Catholic, or else they might get reported. It is useful to compare the perception of Moriscos with the perception of the indigenous peoples in “New Spain”. Whether a Morisco was secretly Muslim may not have mattered because their souls were a lost cause anyway; what mattered were the souls of the indigenous peoples, who were vulnerable to “corruption” by Muslim ideas. For example, Friar Sotomayor was concerned about this, so he filed complaints against the Morisca Catalina de Ibiza and her children for being so disruptive of Mass (Cook 90). If the Inquisition could scare Muslims into thinking that their neighbours could report on them (which they very much did, like in the case of Pedro Hernández (Cook 96)), they would keep their ideas to themselves and thus stop them from propagating. The Inquisition and the colony as a whole stand to lose power if they cannot maintain at least the impression of spiritual orthodoxy, considering that a major justification for the colonial project hinged on the Christian belief that these lands were given to Europeans by God and it is their mission to “save" the "primitive” indigenous populations.
Sorry for this long response; I hope it may be of some use. Of course, this is only one approach to some of your questions, so please feel free to add to it or contest it if you or anyone else would like to!