All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We ask Allah to make us and you steadfast on His Religion till we meet Him. Praise be to Allah, dear sister, for bestowing on you this great Blessing that is Islam. Indeed no blessing is greater than becoming a Muslim. So, do not despair for your past.
On the other hand, know that it is strictly prohibited for the Muslim woman to remain under the custody of a non-Muslim husband. Allah Says (what means): {…they are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them…} [Quran 60:10]
So, the marriage contract between you and this disbeliever is automatically annulated by you becoming a Muslim unless he becomes a Muslim as well.
In such case, there is no need to renew the marriage contract. As for your relation with this non-Mahram Muslim man, if you can get in contact with some Muslim women through Islamic centers, Internet or other means, then that is better for you and you should make your contacts exclusively with them. If you cannot find women to help you and socialize with you about Islamic matters, then there is no objection to your remaining in contact with this man provided you avoid staying with him in seclusion and provided you adhere to Islamic rites such as Hijab and avoiding to be lenient in speech, …etc. But communicating with this man through Internet is better than communicating with him directly as this is better to avoid Satan's insinuations. We draw your attention to the fact that this communication should not exceed the limits of the Sharee’ah and become a friendship in its contemporary meaning.
Indeed such friendship is a gate through which Satan drives people to what is forbidden.
Allah Says (what means): {… and do not follow the footsteps of Satan. Indeed, he is to you a clear enemy.} [Quran 2:168]. We also remind you that Islamic centers are - most of time - good sources for authentic knowledge. So, we advise you to keep on visiting them and looking for pious Muslim women who would be of much help for you as would be reading books, listening to cassettes and corresponding with female preachers all over the world.
Allah knows best.