All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
We ask Allaah The Almighty to guide everyone to the right path and grant them steadfastness in religion.
Allaah The Almighty is Wise in His creation and command. There is a rationale behind every creation and order, whether we are aware of it or not.
While it is a good thing that a Muslim tries to find the rationale behind every creation and order so that his faith increases, it should be known that he would not be able to know the rationale behind some of them. In this case, one should say, {We believe in it. All [of it] is from our Lord. [We hear and we obey]}. He should remember this verse (which means): {He is not questioned about what He does, but they will be questioned.} [Quran 21:23]
Moreover, there are many books discussing the rationale behind certain Sharee‘ah rulings.
Now we will briefly address some of the misconceptions mentioned in the question:
1- She said that religion must conform to reason. This is correct; however, sometimes one may find a contradiction between religion and reason. In this case, religion takes precedence over reason due to the fact that Allaah The Almighty, who knows everything, revealed this religion, whereas our reason cannot comprehend all things.
2- She said that Muslims must know everything to be convinced about Islam. It is a good thing that a Muslim tries to find the rationale behind every creation and command of Allaah The Almighty as we mentioned above. However, one may encounter some creations and commands and he may not know the rationale behind them. In this case, he has no other choice but to submit and believe in them, even if he does not know the rationale behind them.
3- She asked why Allaah The Almighty ordered us to meet some obligations without mentioning the rationale behind them. The answer is that Allaah The Almighty wants to see whether people will obey Him or not, and also to encourage them to think about what that rationale may be.
4- She said that she wants to worship Allaah The Almighty out of love and fear. This is in accordance with the Quran. Allaah The Almighty Says (what means): {They used to hasten to good deeds and supplicate Us in hope and fear.} [Quran 21:90]. The relationship between Allaah The Almighty and His servants is based upon a mixture of fear, hope and love. However, it is not necessary to know the rationale behind everything in order to develop this relationship. Fear can be developed by thinking about death, the grave, the questioning, punishment and Hell. Hope can be developed by remembering reward, Paradise and forgiveness. Love can be developed by thinking about the creation and remembering the bounties of Allaah The Almighty and His Greatness.
5- She asked why Allaah The Almighty created us although He is in no need of us. The answer is this verse (what means): {[He] who created death and life to test you [as to] which of you is best in deed.} [Quran 67:2]
6- She said that the angels do not have the choice to disobey. This is wrong. They have this choice, yet it is not in their nature to disobey since they were created with a natural disposition to obey Allaah The Almighty, and He has not created in them the lusts that He created in humans.
7- She said that she cannot find anyone implementing Islam in the right way. This generalization is obviously wrong. There are Muslims who implement Islam as well as non-observant Muslims. The fact that a large number of Muslims are non-observant does not mean that Islam does not suit this age. Throughout history, we find that whenever Muslims implemented Islam they became powerful and conquered lands as well as hearts.
8- She said that most observant Muslims always feel depressed and are unsuccessful in their life, whereas those who are non-observant do not feel depressed and are successful in their life. This generalization is absolutely wrong. On the contrary, most observant Muslims feel happy and work efficiently and honestly. By contrast, most non-observant Muslims feel depressed and are not characterized by honesty and other noble characteristics. If a person does not socialize with a certain group of people, he may not be able to understand them.
9- She said that she was faced with many adversities as soon as she started to abide by Islam. These adversities are tribulations from Allaah The Almighty to test whether she is sincere in her adherence to Islam, and also to expiate her sins. The extent of adversity corresponds to the extent of one's religion.
10- She said that a large number of scholars and callers to Islam make Muslims hate religion. This is another incorrect generalization. There are perhaps some scholars and callers who do that. In this case, one should advise them concerning the right approach when dealing with people. However, this is not an excuse for one to stop abiding by Islam or to make generalizations.
Finally, I advise the questioner and her friend to make the acquaintance of some good sisters and female callers to Islam, and ask them about any matters they find perplexing.
We ask Allaah The Almighty to better the affairs of all people.
Allaah Knows best.