Reference your last question, I am going to say something that is very harsh, and while I do not mean to be unkind, I do mean to be blunt and not detour around Jones barn.
Dating someone before you have received a decree of nullity is just plain stupid. There is a lot of urban mythology that decrees of nullity are handed out like candy. The truth is, they are not. So you have no business whatsoever forming a friendship with another individual while the Church still says you are married.
There is an old phrase that there is never a fight between one person - it takes two. You have been in an intense relationship which has failed. Without getting into trying to “find fault”, both parties have some responsibility in the failure of that marriage. It is said that it takes about 2 years on average to deal with the grief of the death of a spouse, and the same should apply to someone who has divorced, if people are actually working on what they did or did not do, or should have done differently in the marriage, That should include as least some professional counseling.
Failure to do that runs a high risk of carrying the same patterns into any new relationship. And no, you cannot be working on the new relationship at the same time. No one except rodeo clowns rides two horses at the same time.
Assuming that you will receive a decree of nullity, you owe it to yourself, as well as anyone in the future you might possibly marry, to sort out what occurred in the prior marriage ans work on those issues. Otherwise, you run a high risk of repeating the same or very similar mistakes. Or, as the saying goes, doing the same thing over and over and expecting a different result in a form of insanity.