Is it OK to marry a lady who has a past of dating married men? The majority of the men she has dated were married men. It also bothers me that she keeps her past a secret.
I don't know what kind of things you think she is keeping secret from you. Should a person tell someone she is thinking of marrying whether she is a virgin or not? Yes, and you should be open about that with her as well. Should she tell you all the details about how many guys and how many times? No, because that doesn't leave the past in the past.
I'm assuming here that she has changed from her past behavior. Hopefully, she recognizes that she was committing adultery or, at least, encouraging men to consider adultery by dating married men. It would not do to marry a woman who doesn't see that behavior as being wrong. Even if you were not a Christian, it is a strong signal that she would consider going out with men even after being married.
Date women who encourage you to be a stronger Christian. Only consider a woman as a possible bride because you are certain that the two of you will spend the rest of your lives together.