Female friends.
If you live with your wife getting the visa for a female is not an issue and yes she can stay with you. If you are married but your wife does not live with you in Dubai or you are single and you want to invite a female friend, lover or whatever to stay with you, there are a couple of things tha you should be aware of. By law you are not allowed to get a "visit" visa for a female unless you are authorize by an immigration officer BUT they always issue the Visa and they don't really ask any questions.
I was a little concerned the first time I requested a Visit visa for my girlfriend, I talked to a female officer in immigration and she said that I was not allowed to bring her over unless authorize by a higher ranking officer. The higher ranking officer was sitting right next to her and he said that it was ok for me to request the visa since I was an EK pilot. The second time I didn't even asked and they issued the visa in 5 minutes.
Don't worry about inviting anybody over for a visit, the visa is very easy to obtain if the passport of you female friend is not on the list of the countrys that requires a visa to enter UAE (if your friend is a USA passport holder She does NOT need to obtain a visa prior to arriving to UAE)