Professor asks me if I have other options (to apply). How should I answer?
It sounds to me like he is just making sure that you will have other options if it turns out the school won't admit you with an outside advisor. I don't think there's any harm at all in telling the truth. If he wants you as a student, the fact you have other options shouldn't make a big difference to how much he is willing to help you in the admissions process. In fact, sometimes having other options can even make you more desirable, as it indicates other people/schools think you are valuable too. (In my case, having other offers allowed me to negotiate a slightly better package at my top choice grad school.) If you're worried that he will be less interested in helping you with your application if he knows you are also looking elsewhere, you could always say that you have applied to/been offered place(s) elsewhere, but that the opportunity to work with him remains your top choice.

Regardless of how you reply to him, however (and as I said, I don't see any reason not to tell the truth), I would say that it's always a good idea to apply to a range of schools. Hopefully you will get in to the school you want and be able to work with him, but if the school has indicated there might be a problem with this (even if you and the professor think they are wrong), you may want to have other options.