Respectfully, I used to live there. Have you? If not, don’t you think I might be slightly more qualified to comment?
When I lived there, I wasn’t married to my now-husband (it was actually illegal to cohabit, though the law has now changed, I gather) so he couldn’t sponsor my visa, so I needed to leave the country every month to renew my tourist visa. Sometimes we’d time it to coincide with going away for a weekend, but the rest of the time, I would get together with people I knew in the same position, and we would carshare to the Omani border, drive over into Oman, do a U-turn and re-enter the UAE. Lots of the other cars doing the same thing were minibuses of foreign prostitutes.
Prostitution is illegal, too, and the penalties are huge, but it doesn’t mean it doesn’t happen. There’s huge demand. About 2/3 of the Dubai population is male.
As regards maids sleeping with their employers, of course it happens. I can’t give you statistics, because, while you could certainly report to the police in the past (when extramarital sex was illegal), you’d be letting your husband in for arrest and potential imprisonment too, so most of the stuff that made the headlines was maids being reported by employers for sleeping with their boyfriends on the premises. If the DH was involved, mostly the wife just took the maid straight to the airport. The usual advice was to supervise her packing and check her bags for stolen items.
There was an entire set of racist Dubai urban myths positioning foreign maids as superficially submissive but in fact desperate for rich expat husbands and prepared to have sex to bag one, about employers specifying ‘plain and over 35’ to recruiters, about ‘headache money’ (new maid arrives and asks employer if her pay will be topped up by ‘headache money’, ie, when the wife doesn’t want to have sex, the DH goes to the maid’s room instead) etc etc.
It was a fascinating place for all the wrong reasons.