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 is His slave and Messenger.
Our answer to your questions will be summarized in the following points:
1- Religion and good moral conduct are the criteria for choosing a spouse; for more benefit, please refer to Fatwa 89506. Therefore, you should not hasten to accept to marry (this man) until you ask trustworthy people about him, and then you should perform the Istikhaarah prayer about him as clarified in Fatwa 81434.
2- The only means to righteousness is faith and the obedience to Allaah. Indeed, the best means to achieve happiness and stability of marital life is that both the spouses know and fulfill the rights of each other. For more benefit on the rights of the spouses towards each other, please refer to Fataawa 83157 and 85308.
3- Each spouse should endeavour to forgive the mistakes of the other and he/she should look to his/her positive character. Abu Hurayrah narrated that the Prophet said: "A believing man should not hate a believing woman (i.e. his wife), if he hates one of her characters, he will be pleased with another.” [Muslim]
4- You should not ask your husband why he divorced his wife as this question may embarrass him. In addition to this, there might be some reasons that are not permissible to mention or which one should not mention. We have already mentioned how to avoid divorce taking place, like the spouses fulfilling the rights of each other and observing the obligations towards one another.
5- This girl is considered a Muslim because the child follows the parent who is best in religion as we clarified in Fatwa 81957, and she is becomes your stepdaughter. However, her mother has no right to foster her because she is non-Muslim. Therefore, this man should endeavour to prevent that woman from fostering his daughter and he should make every effort to nurture her on the creed and morals of Islam. For more benefit, please refer to Fatwa 86163.
6- If this girl or her mother or anyone else hates you, then you should be patient, because the outcome of patience is always good.
7- There is no relation between you and your husband’s first wife, and it is permissible for you to be kind to a non-belligerent non-Muslim. However, if you are harmed by her, then you should threaten her to take the matter to the authorities so that they would repel her harm off you.
8- You should be kind to your husband’s parents, the fact that they are non-Muslims does not prevent you from being kind to them. Indeed, among the best things of being kind to them is to call them to Islam.
9- In our site [Islamweb] there are many beneficial matters by which you may help your husband in learning the matters pertaining to his religion, in addition to the Islamic centres that exist in your country.
10-Patience is an act of worship by which a person gets closer to Allaah, and a Muslim should seek the help of Allaah in order to make him patient. Allaah Says (what means): {And be patient, [O Muhammad ], and your patience is not but through Allaah.}[Quran 16:127] Moreover, if a Muslim tries to be patient, Allaah will enable him to be patient. It is confirmed that the Prophet said: "Whoever seeks to be patient, Allaah will make him patient, and nobody can be given a blessing better and greater than patience.” [Al-Bukhari and Muslim]
Allaah Knows best.