Does divorce occur in the aforementioned cases, with doubt regarding the intention of divorce when stipulating it, the wife's dissimulation in taking an oath, the prior retraction of the stipulated oath of divorce, and the occurrence of a breach of previous oaths of divorce?

As long as you did not intend to effect a divorce when your wife lied, or if there was doubt and hesitation regarding the intention to effect a divorce, then the doubt is not considered, and divorce does not occur due to her lie. This is because a kinayah (allusion) requires the intention to effect a divorce, and doubt about divorce or its condition is based on the certainty of the marriage. If the suspension (of divorce) was intended for threat, emphasis, or prevention, and you did not intend to effect a divorce, then divorce does not occur, but rather an expiation for an oath becomes incumbent.