Is the husband's separation after the secret marriage due to the problems his wife caused considered a religious error, and is his wife's knowledge of his marriage to another woman better for me and for her and for me to obtain my full rights?

The husband is not required to inform his wife of his marriage to another woman. The most sound opinion, after seeking guidance from Allah (istikharah), is to proceed with the matter unless Allah diverts him from it. If the matter leads to divorce, do not despair, for it may be a blessing. Allah Almighty says: "But if they separate [by divorce], Allah will enrich each of them from His abundance."