I do not have research or theories, merely hypotheses.
re: incidence of gay Catholic priests
I speculate that the number of gays in the Roman Catholic priesthood could be disproportionately high due to the RCChurch's prohibitions against homosexual intercourse, thus already commanding faithful (as in faithful to the RCC, if not RC) gays to be celibate. The leap from a celebate civilian life to a celebate priesthood, with a purportedly closer connection to God, is lesser than one from a non-celebate civilian life.
The more effeminate mission of the priesthood, to nurture and take care of the Catholic congregation at large, also endears more toward the stereotypes of gays as nurturers and caregivers.
re: child molestation and rape by Catholic priests
The first point of this media sensation is that it consists of unconsenting sex against children; that in itself increases the likelihood of continuing coverage, particular in the United States.
The second is that the direct perpetrators engaged in this violation in their capacity as priests. The role of the priest as a caregiver and a provider of moral guidance stands in stark contrast to the role of child molester / rapist, the unchained egoist that preys on the presumed weakest and most innocent in society.
That they were part of the most noteworthy international organization in our species thus far probably plays a role (similar to the sexual abuse scandals in the UN, but on a more softly powerful level).
Beyond the association with such a powerful organization, the United States has had and still has an anti-Catholic Protestantism (despite the recent cross-denominational ties between patriarchal traditionalists). The power of US Protestantism vs. US Roman Catholicism probably plays a role, as does the fragmented and less structured nature of US Protestant denominations (there are significant differences between RCC priests and Prot. preachers, such as the source of their social power and the institutional support structure).
The coverup mechanisms, the deliberate secrecy, and the continued de facto acceptance of these criminal indulgences add to our tabloid disgust. These after-the-incident actions and their participants doubly revile us for firstly failing to negatively sanction the direct violators and for secondly allowing these violators to continue in their shadow role as child molesters and rapists.
Whether there is a disproportionate frequency of child molestation / rape by RCC priests, I have no data to work with other than the tabloid revelations.
Whether the RCC's commandment of celibacy for its priesthood affects the degree of such incidents, once again I have no data. We quote it as a commonsensical reason, reducing much of the human agency of RCC priests to biological slavishness. I can infer it as a reason for some individuals, but am loathe to concur that it is the source of most of these violations.
I am far more willing to accuse patriarchal ideas and presumptive perogatives as sources for these violations.
While I have much distaste for the RCC and abhorrence for these violations, I believe that it is necessary to caution against the belief that this is only a problem on the part of the RCC and that the continued RCC-priests-as-child-molester jokes are unfunny (in addition to being without originality).