Was it rape?
Absolutely not. They both consented.
It was morally dubious, but I wouldn't call it rape, exactly.
Yes. Faith committed rape.
Yes. Riley committed rape.
Yes. They both committed rape.
Something else which I will explain in my comment.
Under the cut, I'll expand in a little more detail on each of the options.
1. "Absolutely not". This is the simplest answer. Nobody was struggling or being held down. Nobody was coerced or threatened or drugged. Yes, Faith lied to Riley - but people have been known to lie before when trying to persuade someone into bed, and is "I'm Buffy" really more of a lie than "No, I'm not married" or "I'm really interested in what you've been talking about for the last hour"?
2. Nothing much to say here; this is the middle way answer.
3. "Faith committed rape". I don't know about the State of California, but under English law this would probably be the case. Consent to sex obtained by deception or impersonation is invalid. How that differs from the kind of lies I mentioned in (1) is a difficult question, of course, and would be for a judge to decide. Case law offers R v Williams (1923) where a man persuaded a very naive teenage girl that he could perform a "medical procedure" to improve her singing voice; she agreed to this, but the man was eventually convicted of rape anyway because of the deception involved. (And the moral of the story is: parents, giving your children sex education is a really good thing.) Riley thought Faith was Buffy, and almost certainly would not have consented if he'd known the true situation; when he did find out, he was angry and distressed.
4. "Riley committed rape." This may seem a really strange one at first, but it was inspired by listening to the recent fan discussion about 'Dollhouse', and the claims that the Dolls in that show are repeated rape victims. The argument, therefore, is that Riley is raping Buffy in this scene. Her mind may not be present, but her body is, and it's her body that he's having sex with. Buffy is equivalent to Caroline/Echo and "Faith" is her current imprint. The situation is even worse than that in 'Dollhouse', because (arguably, at least) Caroline consented in advance to what would be done with her body, but Buffy never had that option. As such, if you believe that Caroline is a rape victim in almost every episode of Dollhouse, then surely so was Buffy in 'Who Are You?'.
(The question "Can you be the victim of a crime if it has no effect on you and you don't even know about it?" might come up here, except I can't hear it over the sound of all those falling trees in the forest over there.)
5. If Faith raped Riley and Riley raped Buffy, they're both rapists.
So. Any thoughts?