All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Since you have mentioned that you are a religious Muslim woman, then we believe that you certainly believe in the existence of Allah Almighty, and that what you feel is only an insinuation of the devil which he casts in your heart in order to confuse you; this is nothing but one of the plots (evil tricks) of the devil.
You have to repel these whispers and not give in to them; if you do so, then they will not harm you.
Ibn ‘Abbaas narrated that a man came to the Prophet and said: "O Prophet of Allah, one of us finds in himself [satanic whispers about Allah] and feels so bad that he would rather burn until he becomes like charcoal than to reveal what he is thinking about." Thereupon, the Prophet said: 'Allahu Akbar, Allahu Akbar, Allahu Akbar! Al-Hamdu Lillaah (praise be to Allah) Who limited his [devil’s] plots to whispers only!'" [Abu Daawood]
Additionally, repelling the whispers of the devil is a good sign. Abu Hurayrah narrated that some companions of the Prophet came to him and asked: "We find in our hearts what we consider as a very serious matter and a great sin to talk about." The Prophet said: 'Do you really feel this?' They replied, 'Yes.' He remarked: 'This is (a sign of) correct belief.'" [Muslim]
There is no harm for a Muslim to ask in order to increase his certainty (faith), Allah Says (what means): {And [mention] when Abraham said, “My Lord, show me how You give life to the dead.” [Allah] said, “Have you not believed?” He said, “Yes, but [I ask] only that my heart may be satisfied.”} [Quran 2:260]
There is no doubt about the existence of Allah. There are many evidences in the religious texts and in His Sharee’ah (which can only be legislated by the creator, because of the wisdom and mercy in them). There are also many cosmic Signs proving His existence. We have highlighted some of these signs in Fataawa 347611, 85461 and 85823, so please refer to them.
Also, the evidence that Islam is the true religion is highlighted in the following Fataawa 86091, 16595, 88906 and 173389.
This is regarding your first question. As for your second question, please send it to us separately so that we can issue a separate answer for it as per our policy in our site.
Allah knows best.