In the case of the first pair of sentences, I would say #1 is best. In the second case, I would say that #2 is best, but that "Several women have complained of being sexually harassed." would be an alternative.

Hi there, 1. "Celebrities always complain of having no privacy in private locations." 2. "Celebrities always complain of no privacy in private locations." We use "have / having" to indicate our possession of something, be it something concrete (e.g I have some cash in the bank.) or something abstract (e.g I have an inner sense of peace.). As privacy is something we can either have or not have, sentence 1 is more complete in meaning. 1."Several women have complained of having sexual harassment." 2. " Several women have complained of sexual harassment." In contrast, people do not own or possess sexual harassment. It is something that is done to them against their will. Therefore, sentence 1 sounds odd and sentence 2 sounds more natural. Alternatively, we can also write: "Several women have complained of being sexually harassed." In this alternative sentence, "sexually" becomes an adverb modifying the adjective "harassed". In turn, "harassed" describes the noun "women". Hope this helps. Lance