Is the aforementioned marriage Islamically valid, given doubts regarding the contract's authenticity, the number of witnesses, and the followed jurisprudential school of thought? And is seeking divorce considered an injustice to the pregnant wife, in light of the mentioned problems and her lack of religious uprightness?

The question is unclear, but if the marriage was contracted with the testimony of two upright witnesses, along with offer and acceptance, then the marriage contract is valid.

We advise you to keep your wife and try to reform her from the sins you mentioned. Islamic law encourages keeping a wife even if she is disliked, based on the Almighty’s saying: "And live with them in kindness. For if you dislike them - perhaps you dislike a thing and Allah makes therein much good." [An-Nisa:19], and the Hadith: "Let not a believing man hate a believing woman; if he dislikes one of her characteristics, he will be pleased with another."

Furthermore, keeping her achieves the best interest of the fetus, which is to be raised between its parents. If you find it unbearable to live with her, you may divorce her. However, if she does not respond by abandoning sins, then you must divorce her, as it is not desirable to keep such a woman.