Does the wife become forbidden, necessitating a new marriage contract and dower, if the husband said: "You are forbidden to me if you do such and such," and she did that, and then he cohabited with her years after this statement, knowing that he was unaware that what he said was considered a divorce?

The prohibition of a wife depends on the husband's intention. If he intended dhahār (a pre-Islamic form of divorce), it is dhahār. If he intended divorce, it is divorce. If he intended an oath, it is an oath. Similarly, if he made an unqualified statement without intending anything, it is an oath. Therefore, if your intention was not divorce, then no divorce has occurred, and you are obligated to perform an expiation for breaking an oath (kaffārat yamīn).