Is it permissible to seek marriage with a woman who is married to a Muslim man who does not observe her rights and does not adhere to the teachings of Islam, and does the saying, "What is built upon falsehood is false," apply to the relationship that has developed between them?

You must immediately cut off your relationship with this woman, and refrain from messaging or speaking with her. As for her problems with her husband, they are her responsibility, and speaking with her may only worsen the matter. Beware lest Satan cause you to fall into sin under the pretext of offering her advice, for the saying of the Prophet, peace and blessings be upon him, might apply to you: "He who corrupts a woman against her husband is not of us."