From what you have provided I would say No and No. He could be either way. There are a fair number of people that act this way toward family members, especially moms to sons when the father is not in the picture.
Another question would be, "Why do you see this as an issue?"
It sounds like your wife and your son have a very close and open relationship. Reading your post, it certainly sounds like you are concerned, and perhaps have issues on what your son's personality and behaviour may imply about his sexuality. It sounds like their relationship may not be the norm, but not abnormal, if that makes sense. I am picking up that there may be some friction or distance between you and your son. In your post you did not describe your own relationship with him, I find this interesting. I am curious about your attitudes regarding your son's perceived sexual orientation. Would you be accepting of him if he were gay or bisexual? Would you be accepting of him if he were transgender? I cannot make assumptions about if he is or isn't and that is not my place to do.
I have worked with LGBTQ youth and their families in the past. I can tell you that there is a grief and loss cycle experienced by parents of LGBTQ youth. I have seen parents whom consider themselves accepting of LGBTQ people have disappointed or denial responses to their own children. This is rooted in the ideas we have attached to our kids when they are young. If we have sons, we may fantasize about their lives as adults usually placing ideals such as their future wife, children, job, etc. as an example. It is very natural to do as a parent. If our kids start to show behaviours which are not congruent with those ideas, it can make us uncomfortable. The idea that your wife is comfortable with your sons eccentric behaviours may leave you feeling isolated, and frankly, feeling a bit off about the whole thing, including her relationship with him.
I don't like to make assumptions, but I am going to make one now. You love your kid, and you love your wife. I do not know if you are in the place to accept having a child whom MAY be gay or perhaps identify as female, only as a possibility (because again, I cannot make that conclusion how he identifies). My hope is that if that were the case you could accept that. Although as I mentioned it is natural to feel uncomfortable with the idea. I hope that your relationship with your wife is strong enough that you can have a discussion with her about this. It is also natural that their relationship as you describe it can come off as bizarre to you. Life is full of uncomfortable conversations. I hope that you can have a meaningful and non-judgmental conversation about this as it sounds like you have some off feelings from the whole thing. Really, it is about visiting your discomfort about the situation at hand that I think will give you the answer.