The question: I want to ask is of utmost importance to me and I would appreciate if it can be answered as soon as possible.
I married my wife ten years ago. She was born in a family where father is an atheist and mother is a non-practising Christian belonging to Armenian Church. My wife is educated and makes opinion about the things on logic. She accepted Islam because she never believed that Jesus could be son of God. Her belief about other aspects of faith was not clear. We married in a mosque after she said Shahadah, hoping things will improve with time.
In last ten years she has always called herself a Muslim though does not like a label. She supports all the Muslims and Muslim causes, fasts in the month of Ramadan and does not indulge in any Haram things at all. Our children are good Muslim children. She facilitates it as much as possible. I must admit that she herself does not say prayers and I avoid putting too much pressure although I myself adhere to five pillars of Islam with good faith, Insha Allah.
Other day I expressed desire to go to Mecca and she showed hesitation that it is not for her. I got concerned. To check her faith I asked her:
1. Do you believes in God she said yes.
2. All the Prophets she said yes and Muhammad (SAW) being the last one, she said so far yes.
3. Qur’an is the Word of God, she remained silent.
4. Angles, again she remained silent.
5. Day of Judgment and life after and she said, there must be otherwise why we are here.
Because her faith is incomplete I decided that I should put a hold on our husband and wife relationship till the matter is clear.
Am I still married to my wife?
I think there is room for improvement but it will take a lot of talking and convincing. But if there is no change will that much faith allow us to remain married.
I know under force she will say yes to every thing but I do not want to do that.
Please advise urgently.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Your question consists of many matters.

First, the matter of the negligence of the prayers of your wife, if she believes that they are obligatory, Muslim scholars have different opinion concerning the person who neglects the prayers without denying their obligation.  The majority of Muslim scholars are of the opinion that she commits a minor Kufr that does not take her away from Islam, but she is in a great danger.

Some others are of the opinion that if the ruler asked her to repent from neglecting prayers and she does not make repentance then she becomes Kafir. 

A third group is of the opinion that whoever neglects prayers becomes Kafir.

Second, we cannot take any decision about her hesitation in the matter of Hajj; maybe due to a defect in her faith or maybe for another reason.

Third, as for her saying ‘So far yes’ when she is asked about the finality of the Prophet (Sallallahu Alaihi wa Sallam), it indicates that she may change her faith in future, no doubt if she means that, then it is Kufr and apostasy from Islam.  If she says so meaning something else then we cannot conclude her Kufr.

Fourth, as for her keeping quiet when she is asked about Qur'an whether it is the word of Allah or not, we do not know why she kept quiet whether it was due to affirmation or negation so, based on her keeping quiet we cannot issue any decree.

Finally, our advice is to try your best to explain to her the Islamic faith in a good and pleasant manner.

However, if it is proved without any doubt that she does not believe in Angels, in Qur'an and that she may change her faith regarding the Prophet (Sallallahu Alaihi wa Sallam) Muhammad then it is apostasy from Islam and the marriage with her will be cancelled from that time.

If she repents from that during her Iddah you may take her back without any new contract according to the preponderant opinion of Muslim scholars.

If she repents after her Iddah is completed then if you want to take her back, you have to renew the marriage contract fulfilling all the conditions of a valid marriage.

Also, we advise you to provide her with Islamic books, cassettes, articles that address her doubts.  It is better to arrange meetings with the scholars who can remove her doubts and help her understand Islam well.

We supplicate Allah to correct your wife and guide her to the right path.

Allah knows best.