Is divorce permissible in the cases mentioned, and is it the solution, taking into account the deterioration of the husband's health after marriage and his affliction with major diseases, and the wife's suffering from loud gas emissions during sleep, and the widening of the vagina and the emission of strange sounds during intercourse, in addition to her frequent resort to lying?

Divorce is permissible, especially if there is a need for it. It is disliked if there is no need, and it may even be forbidden. A wife can sometimes be a cause of bringing evil, but this is not necessarily always the case. What you mentioned about gas can be treated, so we advise you to be patient with her. If you can marry another woman and keep her, then do so. If you see that divorcing her serves a benefit, then there is no harm, as divorce can sometimes be better if cohabitation becomes impossible and the continuation of the marriage is purely corrupting. A wife lying to her husband may sometimes be permissible under certain conditions.