Have I committed a sin by marrying a married man, despite my happiness with him, and am I burdened with guilt because his wife does not live with him, even though she has not been divorced?

There is no objection to marrying a married man, and there is no injustice to his wife in that. He must be just among his wives, and it is proper to remind him of the obligation to be just between them in the due rights, except for what one of them willingly relinquishes.