Is it permissible to marry a woman who is already married after she converts to Islam, and will a person's prayer for Islam be accepted despite his committing sins?

Familiarity, conversation, and correspondence between foreign men and women without a valid need is a gateway to fitnah (temptation/strife) and corruption, and it must be stopped. Inviting people to Islam is one of the best righteous deeds, as Allah the Almighty says: "And who is better in speech than one who invites to Allah and does righteousness and says, 'Indeed, I am of the Muslims.'" (Surat Fussilat, 41:33). And for Allah to guide one man through you is better for you than red camels. However, the invitation must be through lawful means and with a sincere intention for the sake of Allah. If the woman embraces Islam and her iddah (waiting period) expires, it is permissible to marry her, while observing legal procedures.