Is it permissible for the husband to swear by Allah or to pledge in court that he will not divorce verbally except in front of witnesses or with documentation, with the wife's knowledge and to reassure her?

A husband may swear an oath of divorce. If he breaks it, he must offer expiation for the oath, and the divorce takes effect unless it was not pronounced in the manner he swore by. It also takes effect if he writes such an undertaking before a judge or other authority, unless he was compelled to utter the divorce, in which case he may call two or four witnesses to attest that he will pronounce the divorce without intending it. This is known as "istir'a" (seeking to have witnesses attest to one's intention).